B-orbits of nilpotent order 2 and link patterns

2007/03/13 by Anna Melnikov, Melnikov, Anna · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0703371

openalex publication_date 2007/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the computations of the closures of orbital varieties of nilpotent order 2 and intersections of components of a Springer fiber of nilpotent order 2. In particular we connect our results to the combinatorics of meanders and Temperley-Lieb algebras.

Citations

• Intersections of components of a Springer fiber of codimension one for the two column case

Cited by

• Combinatorial Gelfand Models

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