Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form

G. Felder; R. Rimanyi; A. Varchenko

Home/Archive/arXiv

arXiv · math/0502296

Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form

G. Felder·R. Rimanyi·A. Varchenko

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the canonical U(\n)-valued elliptic differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of elliptic KZ differential equations and Bethe ansatz constructions. We explicitly determine the coefficients of the projections in the simple Lie algebras A_r, B_r, C_r, D_r in a conveniently chosen Poincare-Birkhoff-Witt basis. As an application we give a new formula for eigenfunctions of Hamiltonians of the Calogero-Moser model.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

G. Felder, R. Rimanyi, A. Varchenko. 2005-02-16. Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form. https://arxiv.org/abs/math/0502296

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↗