[图书][B] Crystal bases: representations and combinatorics
D Bump, A Schilling - 2017 - books.google.com
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 …
point of view. Crystal base theory was developed by Kashiwara and Lusztig from the …
Combinatorial descriptions of the crystal structure on certain PBW bases
B Salisbury, A Schultze, P Tingley - Transformation Groups, 2018 - Springer
Using the theory of PBW bases, one can realize the crystal B (∞) for any semisimple Lie
algebra over C using Kostant partitions as the underlying set. In fact there are many such …
algebra over C using Kostant partitions as the underlying set. In fact there are many such …
[HTML][HTML] Categorical crystals for quantum affine algebras
M Kashiwara, E Park - Journal für die reine und angewandte …, 2022 - degruyter.com
In this paper, a new categorical crystal structure for the quantum affine algebras is
presented. We introduce the notion of extended crystals B^ 𝔤(∞) for an arbitrary quantum …
presented. We introduce the notion of extended crystals B^ 𝔤(∞) for an arbitrary quantum …
Crystal base of the negative half of the quantum superalgebra Uq (gl (m| n))
We construct a crystal base of U q (gl (m| n))−, the negative half of the quantum
superalgebra U q (gl (m| n)). We give a combinatorial description of the associated crystal B …
superalgebra U q (gl (m| n)). We give a combinatorial description of the associated crystal B …
Combinatorial Auslander-Reiten quivers and reduced expressions
S Oh, UR Suh - arXiv preprint arXiv:1509.04820, 2015 - arxiv.org
In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quiver for
commutation classes $[\widetilde {w}] $ of $ w $ in finite Weyl group. This combinatorial …
commutation classes $[\widetilde {w}] $ of $ w $ in finite Weyl group. This combinatorial …
Elementary construction of Lusztig's canonical basis
P Tingley - arXiv preprint arXiv:1602.04895, 2016 - arxiv.org
In this largely expository article we present an elementary construction of Lusztig's canonical
basis in type ADE. The method, which is essentially Lusztig's original approach, is to use the …
basis in type ADE. The method, which is essentially Lusztig's original approach, is to use the …
Towards a Combinatorial Model for -weight Multiplicities of Simple Lie Algebras
C Lecouvey, C Lenart, A Schultze - arXiv preprint arXiv:2110.15394, 2021 - arxiv.org
Kostka-Foulkes polynomials are Lusztig's $ q $-analogues of weight multiplicities for
irreducible representations of semisimple Lie algebras. It has long been known that these …
irreducible representations of semisimple Lie algebras. It has long been known that these …
Rigged configurations and the -involution
B Salisbury, T Scrimshaw - Letters in Mathematical Physics, 2018 - Springer
Rigged configurations and the $$*$$ -involution | SpringerLink Skip to main content
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Advertisement SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home …
Crystal base of the negative half of the quantum superalgebra
We construct a crystal base of $ U_q (\mathfrak {gl}(m| n))^-$, the negative half of the
quantum superalgebra $ U_q (\mathfrak {gl}(m| n)) $. We give a combinatorial description of …
quantum superalgebra $ U_q (\mathfrak {gl}(m| n)) $. We give a combinatorial description of …
[图书][B] Comparing two perfect bases
A Dranowski - 2020 - search.proquest.com
Comparing two perfect bases by Anne Dranowski A thesis submitted in conformity with the
requirements for the degree of Doctor of Page 1 Comparing two perfect bases by Anne …
requirements for the degree of Doctor of Page 1 Comparing two perfect bases by Anne …