Kashiwara on crystal bases

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August undefined, 2024

WebbCrystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. WebbThe final chapters of the book describe the Kashiwara-Lusztig theory of so-called crystal (or canonical) bases in representations of complex semisimple Lie algebras. The choice of the topics and the style of exposition make Jantzen's book an excellent textbook for a one-semester course on quantum groups.

Crystal Bases: Representations And Combinatorics - Google Books

WebbOn the polytope defined in [FFL11], associated to any rectangle highest weight, we define a structure of an type -crystal. We show, by using the Stembridge axioms, that this crystal is isomorphic to the one obtained fr… WebbThe Kirillov–Reshetikhin modules Wr,s are finite-dimensional representations of quantum affine algebras U′q(g), labeled by a Dynkin node r of the affine Kac–Moody algebra g and a positive integer s. In this paper we study the combinatorial structure of the crystal basis B2,s corresponding to W2,s for the algebra of type D(1)n. mercs io

Crystal Bases Mathematical Association of America

Webb4 juni 1998 · M. Kashiwara, “ On crystal bases of q-analogue of universal enveloping algebras,” Duke Math. J. 63, 465 ... WebbKashiwara's earlier paper On crystal bases of the q-analogue of universal enveloping algebras. This contains Kashiwara's "grand loop argument" proving that the theory of crytsal bases actually works. Chari and Pressley, Chapter 14.1 has some material, but does not contain everything we need. Webb15 okt. 1998 · Following Kashiwara's algebraic approach in one-parameter case, we construct crystal bases for two-parameter quantum algebras and for their integrable … how old is geraint vincent

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WebbDownload or read book Introduction to Quantum Groups and Crystal Bases written by Jin Hong and published by American Mathematical Soc.. This book was released on 2002 ... the theory of ``crystal bases'' or ``canonical bases'' developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to … Webb30 juni 1991 · The crystal base has a structure of a colored oriented graph, named crystal graph. The crystal base of the tensor product (respectively the direct sum) is the tensor … how old is gerald croft inspector callsWebb17 jan. 2024 · This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by … how old is gerald giraffe

"WebbFebruary 1994 Crystal bases of modified quantized enveloping algebra. Masaki Kashiwara. Duke Math. J. 73(2): 383-413 (February 1994). DOI: 10.1215/S0012-7094 … " - Kashiwara on crystal bases

Kashiwara on crystal bases

COMBINATORICS OF CANONICAL BASES REVISITED: STRING …

WebbCrystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. WebbCrystal bases or Kashiwara crystals are combinatorial structures that mirror repre-sentations of Lie groups. Historically, crystal bases were developed independently …

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Webb6 nov. 1998 · T. Nakashima, “ Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras,” Commun. Math. Phys. 154, 215– 243 (1993). Google Scholar Crossref; 10. M. Kashiwara, “ The crystal base and Littelmann’s refined Demazure character formula,” Duke Math. J. 71, 839– 858 (1993). Google … WebbDual canonical bases for the quantum special linear.... 1. Introduction The theory of crystal and canonical bases was initiated and developed by Kashiwara [9, 10] and Lusztig [14, 17]. Many remarkable ... Notes on affine canonical and monomial bases. We investigate the affine canonical basis and the monomial basis constructed in [LXZ] in …

WebbCrystal bases and categorificationsMasaki KashiwaraAbstract: A crystal basis is a basis at q=0 of the half U−q (g) of a quantum group U q (g) . It lifts ... Webb12 dec. 2007 · M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J. 63 (1991) 465-516. M. Kashiwara , The Riemann-Hilbert problem for holonomic systems, Publ. RIMS, Kyoto Univ. 20 (1984) 319-365.

WebbMasaki Kashiwara is working on algebraic analysis, and recently on quantum groups. The most beautiful result is the introduction of the "Crystal Bases". This is obtained by a … Webb8 juni 1996 · [Submitted on 8 Jun 1996] Geometric Construction of Crystal Bases Masaki Kashiwara, Yoshihisa Saito We realize the crystal associated to the quantized …

WebbQuantum queer superalgebras, crystal bases, odd Kashiwara operators Introduction For the past 30 years, one of the most striking and inﬂuential developments in combina-torial representation theory was the discovery of crystal bases for quantum groups and their representations [10,11]. Right after that discovery, the crystal basis theory attracted

Webb7 sep. 2024 · M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 465–516. Article MathSciNet Google Scholar M. Kashiwara, The crystal base and Littelmann’s refined Demazure character formula, Duke Math. J. 71 (1993), 839–858. Article MathSciNet Google Scholar mercs manitobaWebb22 dec. 2009 · Kashiwara, M.: Global crystal bases of quantum groups. Duke Math. J. 69, 455–485 (1993) Article MATH MathSciNet Google Scholar Kang, S.-J.: Quantum deformations of generalized Kac–Moody algebras and their modules. J. Algebra 175, 1041–1066 (1995) Article MATH MathSciNet Google Scholar how old is geraldine slatteryWebbUn dels pilars de la teoria de la representació dels grups quàntics (i les seves aplicacions a la combinatòria) és la teoria de Crystal Base de Kashiwara. Aquestes són bases altament invariants que són molt adequades per a descomposicions de productes tensorials. En un article amb S.-J. Kang i M. Kashiwara, Benkart va estendre la teoria ... mercs isle wikiWebb11 mars 2024 · M. Kashiwara, On crystal bases, in Canadian Math. Conf. Proc., vol. 16, (Providence, RI), p. 155-197, AMS, (1995). G. Grojnowski and I. Lusztig, A comparison … how old is gerald flurryWebbIn particular, the theory of ``crystal bases'' or ``canonical bases'' developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups. The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases ... how old is gerald croftWebbON CRYSTAL BASES OF THE Q-ANALOGUE OF UNIVERSAL ENVELOPING ALGEBRAS M. KASHIWARA To the memory of Professor Michio Kuga who taught me … how old is gerald lunzWebbarXiv:math/0201143v1 [math.QA] 16 Jan 2002 An algorithm for computing the global basis of an irreducible U q(sp 2n)-module C´edric Lecouvey [email protected] Abstract We d how old is gerald morgan jr