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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
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：Affine Grassmannians for G_2
仿射 格拉斯曼代数 G_2
2023/4/14
I will talk about affine Grassmannians for the exceptional group of type G_2. This group can be given as automorphisms of octonion algebras. I consider all maximal parahoric subgroups in G_2, and give...
This paper is the sequel to The radiance obstruction and par-
allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984),
629 649) which introduced a new family of secondary characteristi...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. In the case of real groups, the
results refer to J. Adams, P. Trapa, M. vanLeuwen, W-L. Yee a...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. This conforms to the Lefschetz
principle which states that what is true for real groups is al...
Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）
affine Weyl groups left cells hyperplanes
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.
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
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...
On stably free modules over affine algebras
stably free modules affine algebras Grothendieck-Witt groups symplectic Witt groups
2011/8/25
Abstract: We prove that stably free modules of rank d-1 over a smooth affine algebra of dimension d over an algebraically closed field k are free, provided (d-1)! is nonzero in k.
New Irreducible Modules for Heisenberg and Affine Lie Algebras
Irreducible Modules Heisenberg Affine Lie Algebras
2011/8/25
Abstract: We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie a...
Denominator identity for affine Lie superalgebras with zero dual Coxeter number
Denominator identity affine Lie superalgebras zero dual Coxeter number
2011/2/28
We prove a denominator identity for non-twisted affine Lie superalgebras with zero dual Coxeter number.
Symplectic reflection algebras and affine Lie algebras
Symplectic reflection algebras affine Lie algebras
2010/11/23
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products c...
Minimal free resolutions for certain affine monomial c
Minimal free resolutions certain affine monomial
2010/11/23
Given an arbitrary field k and an arithmetic sequence of positive integers m_0<...affine monomial curve parameterized by X_0=t^{m_0},...,X_n=t^{m_n}. In this paper, we conjectur...
Invariant subalgebras of affine vertex algebras
Invariant subalgebras affine vertex algebras
2010/11/15
Let g be a simple Lie algebra of dimension n over C, and let V_k(g) be the universal affine vertex algebra at level k. Suppose that G is a reductive group of automorphisms of V_k(g) for all k in C, an...
Affine Patches on Positroid Varieties and Affine Pipe Dreams (Thesis)
Affine Patches Positroid Varieties Affine Pipe Dreams
2010/11/22
The objects of interest in this thesis are positroid varieties in the Grassmannian, which are indexed by juggling patterns. In particular, we study affine patches on these positroid varieties. Our mai...
Affine cellularity of affine Hecke algebras of rank two
Affine cellularity affine Hecke algebras
2010/11/15
We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig-Xi.