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Spin q-Whittaker polynomials [article]

Alexei Borodin, Michael Wheeler
2017 arXiv   pre-print
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]

Alexander Braverman, Michael Finkelberg
2017 arXiv   pre-print
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]

Roman Bezrukavnikov, Michael Finkelberg
2008 arXiv   pre-print
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

Alexander Braverman, Michael Finkelberg
2017 Journal of the London Mathematical Society  
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]

Alexander Braverman, Galyna Dobrovolska, Michael Finkelberg
2015 arXiv   pre-print
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]

Harald Grobner, Michael Harris
2013 arXiv   pre-print
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

Michael Heumos, Stephen Rallis
1990 Pacific Journal of Mathematics  
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 ( /, =Ind™ 2 "(π®π)®δ s P , n ,n n ,n ( p = we have ( MICHAEL J.  ... 
doi:10.2140/pjm.1990.146.247 fatcat:3eti4d2ohfcnnioqrcpz4jziaq

Michael McClean Ames (1933?2006)

2007 American Anthropologist  
(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

Alexander Braverman, Galyna Dobrovolska, Michael Finkelberg
2016 Advances in Mathematics  
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]

Michael F. Whittaker
2010 arXiv   pre-print
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

Nelson B. Phillips, Zhu-li Wan, Linda Whittaker, Shi-Quan Hu, Kun Huang, Qing-xin Hua, Jonathan Whittaker, Faramarz Ismail-Beigi, Michael A. Weiss
2010 Journal of Biological Chemistry  
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
more » ... 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.
doi:10.1074/jbc.c110.105825 pmid:20181952 pmcid:PMC2852910 fatcat:aattyz7cpjfvle3ro22yfoaal4

Aromatic Anchor at an Invariant Hormone-Receptor Interface

Vijay Pandyarajan, Brian J. Smith, Nelson B. Phillips, Linda Whittaker, Gabriella P. Cox, Nalinda Wickramasinghe, John G. Menting, Zhu-li Wan, Jonathan Whittaker, Faramarz Ismail-Beigi, Michael C. Lawrence, Michael A. Weiss
2014 Journal of Biological Chemistry  
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
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.
doi:10.1074/jbc.m114.608562 pmid:25305014 pmcid:PMC4263875 fatcat:mialqaklandbhbei6rxdfvt47i

Spectral triples for hyperbolic dynamical systems [article]

Michael F. Whittaker
2013 arXiv   pre-print
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]

James J. Walton, Michael F. Whittaker
2021 arXiv   pre-print
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
more » ... p, is homeomorphic to the translational hull of the tiling.
arXiv:2112.07652v1 fatcat:7xsdqonkvjbexhqtwnysv7inqa

Subunit dissociation and metal binding by Escherichia coli apo-manganese superoxide dismutase

Mei M. Whittaker, Thomas F. Lerch, Olga Kirillova, Michael S. Chapman, James W. Whittaker
2011 Archives of Biochemistry and Biophysics  
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
more » ... 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.
doi:10.1016/ pmid:21044611 pmcid:PMC3018548 fatcat:2xyjeo6e2ffxdlkeq56q77gqfy
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