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Spin q-Whittaker polynomials
[article]
2017
arXiv
pre-print
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We introduce and study a one-parameter generalization of the q-Whittaker symmetric functions. ...
Reduction to q-Whittaker polynomials. At s = 0, the spin q-Whittaker polynomials reduce to ordinary q-Whittaker polynomials. ...
Algebraic formulation of spin q-Whittaker polynomials. ...
arXiv:1701.06292v1
fatcat:acbmc2752neebe7gvucawipduq
Weyl modules and q-Whittaker functions
[article]
2017
arXiv
pre-print
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modules over the group G[t] and show that their characters form an eigen-function of the lattice version of the q-Toda integrable integrable system (defined by means of the quantum group version of Kostant-Whittaker ...
(will be inserted by the editor)
Weyl modules and q-Whittaker functions
Alexander Braverman1 , Michael Finkelberg2 ...
[22]) to define the notion of q-Whittaker functions Ψλ̌ (q, z). ...
arXiv:1203.1583v6
fatcat:oinjfxp4rbdy7m32o2xrkgzb2u
Equivariant Satake category and Kostant-Whittaker reduction
[article]
2008
arXiv
pre-print
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description to loop rotation equivariant derived category, linking it to Harish-Chandra bimodules for the Langlands dual Lie algebra, so that the global cohomology functor corresponds to the quantum Kostant-Whittaker ...
Proof : We denote by W − := U ⊗ U (ň − ) ψ the Whittaker U -module. ...
We define the Whittaker U ( [ľ,ľ])- module W − L as U ([ľ,ľ])⊗ U (ň L − ) ψ L . ...
arXiv:0707.3799v2
fatcat:cp72gcdq4zfghjnb55bq5xubua
Twisted zastava and q-Whittaker functions
2017
Journal of the London Mathematical Society
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2015 pre-print arXiv:1410.2365v3 fatcat:w7dt7oq4j5eollulgyzlfutxvqOther Versions
The q-Whittaker functions. LetǦ denote the Langlands dual group of G with its maximal torusŤ . Let W be the Weyl group of (G, T ). ...
We recall the notion of q-Whittaker functions Ψλ(q, z): W -invariant polynomials in z ∈ T with coefficients in rational functions in q ∈ C * (λ ∈ X * (T ) + a dominant weight of G). ...
Fermionic formula and q-Whittaker functions 4.1. Fermionic formula. Recall the setup of Section 2.1. ...
doi:10.1112/jlms.12057
fatcat:7ffrbwpdx5ghfet7v6r7saolgi
Gaiotto-Witten superpotential and Whittaker D-modules on monopoles
[article]
2015
arXiv
pre-print
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As a byproduct we give a natural interpretation of the Gaiotto-Witten superpotential and relate it to the theory of Whittaker D-modules introduced by D.Gaitsgory. ...
In particular, it turns out that the Gaiotto-Witten superpotential [9] admits a natural interpretation in terms of Whittaker D-modules of [8] . 1.2. Quasi-maps. ...
arXiv:1406.6671v2
fatcat:hoxcu67exvfjtamdd6vxvwcuw4
Whittaker periods, motivic periods, and special values of tensor product L-functions
[article]
2013
arXiv
pre-print
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One is defined by the rational structure on topological cohomology, the other is given in terms of the Whittaker model. The ratio between these rational structures is called a Whittaker period. ...
We show that, under certain regularity and polarization hypotheses, the Whittaker period of a cuspidal Π can be given a motivic interpretation, and can also be related to a critical value of the adjoint ...
to GL n , the other from the Whittaker model. ...
arXiv:1308.5090v1
fatcat:oqtqwtpytzd2jlbyrmvq352oim
Symplectic-Whittaker models for Gln
1990
Pacific Journal of Mathematics
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The Whittaker model J£ n 9 o is the only model which has received attention. It was shown by I. M. Gel'fand and D. A. Kazhdan ([Ge-Ka,l]) that the Whittaker model is unique, 247 248 MICHAEL J. ...
Unless stated otherwise, GL« will denote GL Π (F). 250 MICHAEL J. HEUMOS AND STEPHEN RALLIS 252 MICHAEL J. HEUMOS AND STEPHEN RALLIS 2.3. Let / = J n . ...
For f s e I s and the representation
(11.3.1.2.1)
/, =Ind™ 2 "(π®π)®δ s
P
,
n ,n
n ,n
(11.3.1.2.2)
p =
we have
(11.3.1.2
MICHAEL J. ...
doi:10.2140/pjm.1990.146.247
fatcat:3eti4d2ohfcnnioqrcpz4jziaq
Michael McClean Ames (1933?2006)
2007
American Anthropologist
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(Photo courtesy of Clancy Dennehy
for the University of British Columbia, Alumni Affairs)
Michael McClean Ames (1933-2006)
ELVI WHITTAKER
University of British Columbia
Michael Ames, a professor emeritus ...
Whittaker, Elvi, and Michael M
Ames 2006 Anthropology and Sociology at the University of British Columbia from 1947 to the 1980s. Jn Historicizing Canadian Anthropology. ...
doi:10.1525/aa.2007.109.3.589
fatcat:rntusthwjraqbblvdo74pr2i54
Gaiotto–Witten superpotential and Whittaker D-modules on monopoles
2016
Advances in Mathematics
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As a byproduct we give a natural interpretation of the Gaiotto-Witten superpotential studied in [9] and relate it to the theory of Whittaker D-modules discussed in [8]. 2 18 ...
In particular, it turns out that the Gaiotto-Witten superpotential [9] admits a natural interpretation in terms of Whittaker D-modules of [8] .
Quasi-maps. ...
doi:10.1016/j.aim.2016.03.024
fatcat:rzp67e5r4jfq3nxa5grkrtkyri
C*-algebras of tilings with infinite rotational symmetry
[article]
2010
arXiv
pre-print
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A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a separating dense set is exhibited in the C*-algebra which encodes the structure of the topological dynamical system. In the case of a substitution tiling, natural subsets of this separating dense set are used to define an AT-subalgebra of the C*-algebra. Finally our results are applied to the Pinwheel Tiling.
arXiv:1010.1991v1
fatcat:3qtkxzeqvvcsdil3do6mk5vkue
Supramolecular Protein Engineering
2010
Journal of Biological Chemistry
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Bottom-up control of supramolecular protein assembly can provide a therapeutic nanobiotechnology. We demonstrate that insulin's pharmacological properties can be enhanced by design of "zinc staples" between hexamers. Paired (i, i+4) His substitutions were introduced at an α-helical surface. The crystal structure contains both classical axial zinc ions and novel zinc ions at hexamerhexamer interfaces. Although soluble at pH 4, the combined electrostatic effects of the substitutions and bridging
doi:10.1074/jbc.c110.105825
pmid:20181952
pmcid:PMC2852910
fatcat:aattyz7cpjfvle3ro22yfoaal4
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... inc ions cause isoelectric precipitation at neutral pH. Following subcutaneous injection in a diabetic rat, the analog effected glycemic control with time course similar to that of long-acting formulation Lantus ® . Relative to Lantus, however, the analog discriminates at least 30-fold more stringently between the insulin receptor and mitogenic IGF receptor. Because aberrant mitogenic signaling may be associated with elevated cancer risk, such enhanced specificity may improve safety. Zinc stapling provides a general strategy to modify the pharmacokinetic and biological properties of a subcutaneous protein depot. http://www.jbc.org/cgi/
Aromatic Anchor at an Invariant Hormone-Receptor Interface
2014
Journal of Biological Chemistry
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Invariant insulin residue Phe B24 (a site of diabetes-associated mutation) contacts the insulin receptor. Results: Hormonal function requires hydrophobicity rather than aromaticity at this site. Conclusion: The B24 side chain provides a nonpolar anchor at the receptor interface. Significance: Nonstandard aliphatic modification of residue B24 may enhance therapeutic properties of insulin analogs. Crystallographic studies of insulin bound to fragments of the insulin receptor have recently defined
doi:10.1074/jbc.m114.608562
pmid:25305014
pmcid:PMC4263875
fatcat:mialqaklandbhbei6rxdfvt47i
more »
... the topography of the primary hormone-receptor interface. Here, we have investigated the role of Phe B24 , an invariant aromatic anchor at this interface and site of a human mutation causing diabetes mellitus. An extensive set of B24 substitutions has been constructed and tested for effects on receptor binding. Although aromaticity has long been considered a key requirement at this position, Met B24 was found to confer essentially native affinity and bioactivity. Molecular modeling suggests that this linear side chain can serve as an alternative hydrophobic anchor at the hormone-receptor interface. These findings motivated further substitution of Phe B24 by cyclohexanylalanine (Cha), which contains a nonplanar aliphatic ring. Contrary to expectations, [Cha B24 ]insulin likewise exhibited high activity. Furthermore, its resistance to fibrillation and the rapid rate of hexamer disassembly, properties of potential therapeutic advantage, were enhanced. The crystal structure of the Cha B24 analog, determined as an R 6 zincstabilized hexamer at a resolution of 1.5 Å , closely resembles that of wild-type insulin. The nonplanar aliphatic ring exhibits two chair conformations with partial occupancies, each recapitulating the role of Phe B24 at the dimer interface. Together, these studies have defined structural requirements of an anchor residue within the B24-binding pocket of the insulin receptor; similar molecular principles are likely to pertain to insulin-related growth factors. Our results highlight in particular the utility of nonaromatic side chains as probes of the B24 pocket and suggest that the nonstandard Cha side chain may have therapeutic utility. Insulin is a small globular protein critical to the hormonal regulation of vertebrate metabolism (Fig. 1A) (1). Containing two peptide chains, A (21 residues) and B (30 residues), the hormone binds to a receptor tyrosine kinase, designated the insulin receptor (IR) 6 (2). The IR is a disulfide-linked homodimer with subunits (␣) 2 ; the extracellular ␣ subunit binds insulin, whereas the transmembrane  subunit contains an intracellular tyrosine kinase domain (1). The crystal structure of the dimeric ectodomain (␣ ⌬ ) 2 (where  ⌬ designates the extracellular portion of the  subunit) has revealed a ⌳-shaped conformation (Fig. 1B) , whose legs sit upon the plasma membrane (coral disk at bottom) (3). A single insulin molecule binds with high affinity to a tandem site spanning both ␣ subunits (4). This site consists of the N-terminal leucine-rich repeat domain (L1) of one ␣ subunit and the C-terminal segment of the other (␣CT). The structure of insulin bound in a ternary complex . 6 The abbreviations used are: IR, insulin receptor; ␣CT, C-terminal segment of the IR ␣ subunit; IR, domain-minimized model of the insulin receptor; Cha, cyclohexanylalanine; CR, cysteine-rich domain of IR; DM, diabetes mellitus; IGF, insulin-like growth factor; IGF-1R, type 1 IGF receptor; L1, first leucine-rich repeat domains of IR; L1- 2 , central -sheet of the L1 domain; Orn, ornithine; r.m.s.d., root-mean-square deviation; TOCSY, total correlation 1 H NMR spectroscopy; PDB, Protein Data Bank; AOC, area over the curve; MD, molecular dynamics; Amino acids are designated by standard one-and three-letter codes. B24 -DKP]insulin (A) and DKP-insulin (B) is shown. At left are TOCSY spectra of aromatic spin systems; at right are NOESY spectra in region containing cross-peaks between aromatic protons (vertical axis, 2 ) and aliphatic protons, including upfield shifted methyl groups (horizontal axis, 1 ). Brackets/arrows denote aromatic and methyl group resonances with labeled residues. FIGURE 6. Crystal structure of [Cha B24 ,Orn B29 ]insulin. A, R 6 zinc hexamer. The A and B chains are shown in black and green; Cha B24 side chains are highlighted in red. The two axial zinc ions are aligned in the center (blue), coordinated by trimer-related His B10 side chains (white). B, superposition of a representative analog protomer (gray) and WT protomer (white). The side chains of Cha B24 (red) and Phe B24 (white) are shown as sticks. C, stereo view of aromatic residues (gray) and Cha B24 (red) at dimer interface. D, expanded view of the side chains near B24 in the analog structure (gray) and WT structure (white). Sulfur atoms of cysteine A20 -B19 are shown as yellow spheres. Coordinates of the WT R 6 hexamer were obtained from PDB entry 1ZNJ.
Spectral triples for hyperbolic dynamical systems
[article]
2013
arXiv
pre-print
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Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topological entropy of the Smale space.
arXiv:1011.3292v2
fatcat:6dstxpfnmnbsfbw2k5jjombsly
Self-similarity and limit spaces of substitution tiling semigroups
[article]
2021
arXiv
pre-print
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We show that Kellendonk's tiling semigroup of an FLC substitution tiling is self-similar, in the sense of Bartholdi, Grigorchuk and Nekrashevych. We extend the notion of the limit space of a self-similar group to the setting of self-similar semigroups, and show that it is homeomorphic to the Anderson--Putnam complex for such substitution tilings, with natural self-map induced by the substitution. Thus, the inverse limit of the limit space, given by the limit solenoid of the self-similar
arXiv:2112.07652v1
fatcat:7xsdqonkvjbexhqtwnysv7inqa
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... p, is homeomorphic to the translational hull of the tiling.
Subunit dissociation and metal binding by Escherichia coli apo-manganese superoxide dismutase
2011
Archives of Biochemistry and Biophysics
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Metal binding by apo-manganese superoxide dismutase (apo-MnSOD) is essential for functional maturation of the enzyme. Previous studies have demonstrated that metal binding by apo-MnSOD is conformationally gated, requiring protein reorganization for the metal to bind. We have now solved the X-ray crystal structure of apo-MnSOD at 1.9 Å resolution. The organization of active site residues is independent of the presence of the metal cofactor, demonstrating that protein itself templates the unusual
doi:10.1016/j.abb.2010.10.021
pmid:21044611
pmcid:PMC3018548
fatcat:2xyjeo6e2ffxdlkeq56q77gqfy
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... metal coordination geometry. Electrophoretic analysis of mixtures of apoand (Mn 2 )-MnSOD, dye-conjugated protein, or C-terminal Strep-tag II fusion protein reveals a dynamic subunit exchange process associated with cooperative metal binding by the two subunits of the dimeric protein. In contrast, (S126C) (SS) apo-MnSOD, which contains an inter-subunit covalent disulfide crosslink, exhibits anticooperative metal binding. The protein concentration dependence of metal uptake kinetics implies that protein dissociation is involved in metal binding by the wild type apo-protein, although other processes may also contribute to gating metal uptake. Protein concentration dependent small-zone size exclusion chromatography is consistent with apo-MnSOD dimer dissociation at low protein concentration (K D = 1×10 −6 M). Studies on metal uptake by apo-MnSOD in Escherichia coli cells show that the protein exhibits similar behavior in vivo and in vitro.
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