A binary operation on irreducible components of Lusztig's nilpotent\n varieties II: applications and conjectures for representations of GL_n\n over a non-archimedean local field

2021/11/09 by Erez Lapid, Alberto Mínguez, Lapid, Erez +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2111.05162

openalex publication_date 2021/11/09 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In the first part of the paper we defined and studied a binary operation on\nthe set of irreducible components of Lusztig's nilpotent varieties of a quiver.\nFor type A we conjecture, following Geiss and Schr "oer, that this operation\nis compatible with taking the socle of parabolic induction of representations\nof general linear groups over a local non-archimedean field, at least when one\nof the irreducible components is rigid. We verify this conjecture in special\ncases.\n

Cited by

• Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A
• The spectrum of the symplectic Grassmannian and Mat_n,m

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