Cell decompositions of quiver flag varieties for nilpotent representations of the oriented cycle

2015/09/26 by Julia Sauter, Sauter, Julia
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Primary 14M15 #Representation Theory (math.RT) #Secondary 16G20 #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1509.08026

openalex publication_date 2015/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalizing Schubert cells in type A and a cell decomposition if Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation and describe the T-equivariant cohomology using Goresky-Kottwitz-MacPherson-theory. As an application of the cell decomposition we obtain a vector space basis of certain modules (for quiver Hecke algebras of nilpotent representations of this quiver), similar modules have been studied by Kato as analogues of standard modules.

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