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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the lowest two-sided cells of affine Weyl groups
仿射Weyl群 最低双侧胞 Kazhdan-Lusztig基
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2023/12/11
In this talk, I will present a proof a decomposition formula of Kazhdan-Lusztig basis for the elements in the lowest two-sided cell of an affine Weyl group. This formula can be used to determine the l...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-abelian Derived Categories and Derived Schur and Weyl Functors
非阿贝尔派生范畴 派生舒尔 外尔函子
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2023/4/13
We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Sc...
Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）
affine Weyl groups left cells hyperplanes
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2011/9/28
Let F be any canonical left cell of the affine Weyl group Wa of type A. We describe the lower boundary hyperplanes for F, which answer two questions of Humphreys.
C型Weyl模的一个新的重数公式
单李代数 重数公式 Weyl模 权
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2011/9/28
利用Littelmann [2], [4] 和叶家琛与周忠国 [5] 所给出的结果和所使用的方法, 本文首先给出了Cl型复单李代数gl的普遍包络代数U(g l)的整形式的一组单项式基, 并构造了它的子代数的一个滤链. 在此基础上, 本文得到了U(g l)的 Weyl 模 V(λ) 的整形式的一组新基以及计算其权空间维数的一个新的重数公式.
Left cells with a-value 4 in the affine weyl groups Ei(i=6,7,8)
two-sided cell left cell a-function distinguished involution left-connected
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2011/9/28
In the present paper,we give the respresentative set of left cell with a-value 4 in the affine weyl groups Ei(i=6,7,8),and the distinguished involution.Then we show that these left cells are left-conn...
Weyl modules for multiloop algebras
Weyl modules multiloop algebras
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2011/2/25
Global and local Weyl modules for the untwisted multiloop Lie algebras were defined in [CFK] via homological properties. In this paper we extended the ideas to give a categorical definition of the Wey...
Patterns in Wigner-Weyl approach
Patterns Wigner-Weyl approach
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2010/12/28
We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoheren...
Extension of Symmetric Spaces and Restriction of Weyl Groups and Invariant Polynomials
Invariant polynomials Extension of symmetric spaces Spherical Fourier transform
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2011/1/17
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant poly-nomial.
Patterns in Wigner-Weyl approach
Patterns Wigner-Weyl approach
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2011/3/3
We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoheren...
Weyl modules, Demazure modules and finite crystals for non-simply laced type
Weyl modules Demazure modules finite crystals non-simply laced type
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2011/2/28
We show that any Weyl module for a current algebra has a filtration such that each successive quotient is isomorphic to some Demazure mod-ule.
On certain varieties attached to a Weyl group element
certain varieties Weyl group element
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2011/1/20
0. Introduction and statement of results 0.1. Let k be an algebraically closed field. Let G be a connected reductive algebraic group over k. We assume that we are in one of the following two cases.(1)...
The Non-Compact Weyl Equation
Non-Compact Weyl Equation
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2011/3/4
A non-compact version of the Weyl equation is proposed, based on the spin zero rep-resentation of the sl2 algebra. Solutions of the aforementioned equation are obtained in terms of the Kummer function...
Universal Groebner Bases in Weyl Algebras
Universal Groebner Bases Weyl Algebras
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2010/11/24
A topological space TO(S) of total orderings on any given set S is introduced and it is shown that TO(S) is compact if S is countable. The set NO(N) of all normal orderings of the nth Weyl algebra W ...
Conjugacy classes in Weyl groups and q-W algebras
Conjugacy classes Weyl groups q-W algebras
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2010/11/17
We define noncommutative deformations W_q^s(G) of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group G which play the role of Slodowy sl...