Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries

Ogul Arslan; Peter Sin

Home/Archive/arXiv

arXiv · 0908.3035

Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries

Ogul Arslan·Peter Sin

View original source ↗Read source document ↗Export metadata ↓

Abstract

We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in finite geometries and knowledge of their dimensions yields the $p$-ranks of these incidence systems.

Explore related subjects

math.RT math.CO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ogul Arslan, Peter Sin. 2023-05-06. Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries. https://arxiv.org/abs/0908.3035

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On singular supports of Lusztig's perverse sheaves

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if and only if its singular support is contained in Lusztig's Lagrangian variety, that is, the variety of nilpotent representations of the preprojective algebra of the quiver.

math.RT↗

arXiv2026

Skein algebras and quantized Coulomb branches

To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a one-holed torus, we describe a relationship between this quantized Coulomb branch and the Kauffman bracket skein algebra of the surface. We formulate a general conjecture relating these algebras.

math.RT↗

arXiv2026

Kernel of Scott modules and Brauer indecomposability

Let $k$ be an algebraically closed field of prime characteristic $p$. Let $G$ be a finite group. We investigate the Brauer indecomposability of Scott $kG$-modules in relation to the kernel of modules. We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott $kG$-module can be lifted from that of a Scott module over a $p$-local subgroup.

math.RT↗