Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.17907

The endoscopic character identity for even special orthogonal groups

Hao Peng
View original source ↗Read source document ↗Export metadata ↓

Abstract

We establish the endoscopic character identity for bounded $A$-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the real Adam--Johnson case by combining local-global compatibility principle with Arthur's multiplicity formula for non-quasisplit even special orthogonal groups established by Chen and Zou in arXiv:2103.07956. This result plays a key role in the author's work arXiv:2503.04623 on the compatibility between the Fargues--Scholze local Langlands correspondence and classical local Langlands correspondence for even special orthogonal groups.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hao Peng. 2026-04-14. The endoscopic character identity for even special orthogonal groups. https://arxiv.org/abs/2506.17907

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↗