On extensions and branching rules for modules close to completely splittable

On some extensions of p-restricted completely splittable GL(n)-modules

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(λ),L_n(μ))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(λ)$ and $L_n(μ)$ are rational irreducible GL(n)-modules with highest weights $λ$ and $μ$ respectively, the restriction of $L_n(λ)$ to any Levi subgroup of GL(n) is semisimple, $λ$ is a $p$-restricted weight and $μ$ does not strictly dominate $λ$.

Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.

Dirac 上同调、分支律与 Wallach 模

Dirac cohomology, branching laws and Wallach modules

本文基于 Dirac 上同调方法，针对例外李群 E_{6(-14)} 和 E_{7(-25)}，从 Dirac 上同调恢复 Wallach 模的 K-谱，推广了 2013 年 Huang 等人的分支律结果。

作为分支规则的局部特征展开：幂零锥与$\n\mathrm{SL}(2)$的情形

The local character expansion as branching rules: nilpotent cones and the case of $\mathrm{SL}(2)$

该研究建立p进群$\n\mathrm{SL}(2,F)$极大紧子群表示的分支规则，给出局部特征展开的表示论类比，并推广至一般连通约化群，证明多类不可约正深度表示的波前集由其未精炼极小$K$-型的幂零支集完全决定。

Quasi-Spin Graded-Fermion Formalism and $gl(m|n)\downarrow osp(m|n)$ Branching Rules

The graded-fermion algebra and quasi-spin formalism are introduced and applied to obtain the $gl(m|n)\downarrow osp(m|n)$ branching rules for the "two-column" tensor irreducible representations of gl(m|n), for the case $m\leq n (n > 2)$. In the case m < n, all such irreducible representations of gl(m|n) are shown to be completely reducible as representations of osp(m|n). This is also shown to be true for the case m=n except for the "spin-singlet" representations which contain an indecomposable representation of osp(m|n) with composition length 3. These branching rules are given in fully explic…

Homology representations of GL(n,q) from Grassmannians in cross-characteristics

Let F* be the field of q elements and let P(n,q) denote the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) for a coefficient field F of positive characteristic co-prime to q. As GL(n,q)-representations these modules are obtained from the permutation action of GL(n,q) on the set of subspaces of F*. We prove a branching rule for the H^{n}_{k,i} and use this to determine the homology representations completely. Results include a duality theorem, the characterisation of H^{n}_{k,i} through the standard irreducible…