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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...
Density and Redundancy of the Noncoherent Weyl-Heisenberg Superframes
Density and Redundancy Noncoherent Weyl-Heisenberg Superframes
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2015/9/29
Density and Redundancy of the Noncoherent Weyl-Heisenberg Superframes.
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case
Stable Case Multiple Dirichlet Series
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2015/7/6
Weyl group multiple Dirichlet series were associated with a root system Φ and a number
field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] an...
Given a root system Φ of rank r and a global field F containing the n-th
roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose
coefficients are n-th ...
Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory
Type A Combinatorial Theory Dirichlet Series
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2015/7/6
Speci cally, two distinct versions of the Gelfand-Tsetlin de nition were given. It
is not apparent that they are equal. Either of these de nitions is purely local in that
it speci es the p-part of t...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
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2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Coefficients of the n-fold Theta Function and Weyl Group Multiple Dirichlet Series
Dirichlet Series Theta Function
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2015/7/6
We establish a link between certain Whittaker coecients of the generalized
metaplectic theta functions, rst studied by Kazhdan and Patterson [14], and
the coecients of the stable Weyl group multi...
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
Rational Function Field Multiple Dirichlet
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2014/12/8
Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreduc...
光滑Weyl和的分数幂均值的数值上界
允许指数 光滑Weyl和 均值 数值上界
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2014/5/5
通过讨论光滑Weyl和的任意幂次均值的数值上界之间的关系,本文给出了幂次为区间[4，5]中的值时相应均值的数值上界的一些新结果.
E6型Weyl群中左胞腔的左连通性
Weyl~群 左胞腔 双边胞腔 左连通性
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2013/3/6
首先通过计算机编程找出~$E_{6}$~型~Weyl~群左胞腔的所有极短元,利用这些极短元证明了~$E_6$~型~Weyl~群的所有左胞腔都是左连通的,从而证明了~Lusztig~关于左胞腔左连通性的一个猜想在~$E_6$~型~Weyl~群中是成立的.
仿射~Weyl~群\,$(\widetilde{C}_4,\,S)$\,可被看成仿射\,Weyl\,群\,$(\widetilde{A}_7,\,\widetilde{S})$~在某个群自同构\,$\alpha$\,下的不动点集合.记\,$\widetilde{l}:\widetilde{A}_7\longrightarrow\mathbf{\mathbf{N}}$\,是仿射\,Weyl\,群\,...
On Titchmarsh-Weyl functions of first-order symmetric systems with arbitrary deficiency indices
First-order symmetric system decomposing boundary triplet Nevanlinna boundary conditions m-function
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2012/6/19
We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'(t)-B(t)y(t)=\D(t) f(t)$ on an interval $[a,b> $ with the regular endpoint $a$. The deficiency indices $n_\pm$ of the ...
We work in both the complex and in the para-complex categories and examine (para)-K\"ahler Weyl structures in both the geometric and in the algebraic settings. The higher dimensional setting is quite ...
For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants...