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A Robinson-Schensted-type correspondence for a dual pair on spinors

Itaru Terada
1993 Journal of combinatorial theory. Series A  
DEDICATED TO PROFESSOR TOSIRO TSUZUKU ON HIS SIXTIETH BIRTHDAY A new Robinson-Schensted-type correspondence is given in connection with a dual pair of type (Cm, C,) on spinors, i.e., the pair (Sp(2m, C  ...  Our contribution lies in the interpretation of this dual pair in a form expressible in terms of insertions, and also in the construction of a bijection that expresses the history of shape changes occuring  ...  The frame might be omitted so that a tableau would be just an array of symbols in the shape 4. A DUAL PAIR OF TYPE (Cm, Cn) ON SPINORS Dual pairs.  ... 
doi:10.1016/0097-3165(93)90027-6 fatcat:6tsq37t2evg6bh72jgs27wmcia

Page 6445 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Bernard Leclerc (F-PARIS7-LI; Paris) 95k:05183 05E15 20G05 Terada, Itaru (J-TOK YOA; Meguro) A Robinson-Schensted-type correspondence for a dual pair on spinors. (English summary) J. Combin.  ...  “In this article, we construct a new bijection connected to ‘a dual pair on spinors of type (C,,,C,)’ in K. Hasegawa’s ter- minology [Publ. Res. Inst. Math.  ... 

Page 39 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Robinson-Schensted for SO(2n) (Japanese) (pp. 61-87); Itaru Ter- ada, A Robinson-Schensted correspondence that corresponds to a dual pair of spinors (Japanese) (pp. 88-104); Toshiki Nakashima, On the  ...  In- stead of the inverse operation method, which fails for fuzzy sets, inverse operations on the boundary points of a-level set intervals for continuous membership functions are used when the derived 92a  ... 

Skew Howe duality and limit shapes of Young diagrams [article]

Anton Nazarov, Olga Postnova, Travis Scrimshaw
2021 arXiv   pre-print
We consider the skew Howe duality for the action of certain dual pairs of Lie groups (G_1, G_2) on the exterior algebra ⋀(ℂ^n⊗ℂ^k) as a probability measure on Young diagrams by the decomposition into the  ...  We prove a combinatorial version of this skew Howe for the pairs (GL_n, GL_k), (SO_2n+1, Pin_2k), (Sp_2n, Sp_2k), and (Or_2n, SO_k) using crystal bases, which allows us to interpret the skew Howe duality  ...  A RobinsonSchensted-type correspondence for a dual pair on spinors. J. Combin. Theory Ser. A, 63(1):90–109, 1993. [TZ04] Tatsuya Tate and Steve Zelditch.  ... 
arXiv:2111.12426v2 fatcat:iczcgd5eujgsldxdxvry6anyui

Classification of primitive ideals of U(o(∞)) and U(sp(∞)) [article]

Aleksandr Fadeev
2020 arXiv   pre-print
Theng(∞)=_n≥ 2g(2n) for g(2n)=o(2n) or g(2n)=sp(2n), respectively.  ...  In the case of sp(∞), only 'half' of the primitive ideals are integrable, and nonintegrable primitive ideals correspond to triples (x,y,Z) where y is a half-integer.  ...  Let's describe the Robinson-Schensted (or Robinson-Schensted-Knuth) algorithm.  ... 
arXiv:2001.03858v1 fatcat:4u5youzrbfcc5m35engrx3tyb4

On ideals in U(sl(∞)), U( o(∞)), U(sp(∞)) [article]

Ivan Penkov, Alexey Petukhov
2016 arXiv   pre-print
We provide a review of results on two-sided ideals in the enveloping algebra U( g(∞)) of a locally simple Lie algebra g(∞).  ...  The main results include a description of all integrable ideals in U( g(∞)), as well as a criterion for the annihilator of an arbitrary (not necessarily integrable) simple highest weight module to be nonzero  ...  This is accomplished by a careful reading of [BV, Section: The Robinson-Schensted Algorithm for Classical Groups]. It remains to compare Steps 5 of the two algorithms.  ... 
arXiv:1511.01733v2 fatcat:trkj77zecrfltcckpsusnl2pgm

Littelmann paths and Brownian paths

Philippe Biane, Philippe Bougerol, Neil O'connell
2005 Duke mathematical journal  
We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.  ...  In the case of a Weyl group of type A d−1 the transform P w0 is connected with the Robinson, Schensted and Knuth (RSK) correspondence : Let us consider a word v 1 v 2 · · · v n written with the alphabet  ...  This last weight corresponds to the spinor representation for type B l , which is a minuscule representation, i.e. all weights are conjugate to ω l .  ... 
doi:10.1215/s0012-7094-05-13014-9 fatcat:2xddowccizaitf2za7gs3gnyzu

Page 385 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
Differential operators on quotients of simple groups. 95i:16027 Tan, Eng-Chye see Aslaksen, Helmer; et al., 95c:15061 Terada, Itaru A Robinson-Schensted-type correspondence for a dual pair on spinors.  ...  Splitting metaplectic covers of dual reductive pairs. (English summary) 95h:22019 Kuhn, Nicholas J. Generic representations of the finite general linear groups and the Steenrod algebra.  ... 

Page 1354 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
(Evangelos Jfantis) 95i:39007 39A70 (42C05, 47A57, 47B39) Terada, Itaru A Robinson-Schensted-type correspondence for a dual pair on spinors. (English summary) J. Combin. Theory Ser.  ...  Primal-dual algorithms for linear programming based on the logarithmic barrier method. (English summary) J. Optim. Theory Appl. 83 (1994), no. 1, 1-26.  ... 

The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography [article]

Matthias Christandl
2006 arXiv   pre-print
In particular, it is shown how to derive a one-to-one relation between the spectra of a bipartite quantum state and its reduced states, and the Kronecker coefficients of the symmetric group.  ...  Drawing on an analogy between entanglement distillation and secret-key agreement in classical cryptography, a new entanglement measure, 'squashed entanglement', is introduced.  ...  33 equivalent, xxi external product, xxv fundamental, 43 irreducible, xxii Lie group, 17 regular, xxv spin, 20 tensor product, xxv reverse relative entropy of entanglement, 106 ring of invariants, 42 Robinson-Schensted  ... 
arXiv:quant-ph/0604183v1 fatcat:uc2tsnbnevgwne2y7wyquptyyu