Quantum invariants for decomposition problems in type A rings of\n representations

2017/11/05 by Maxim Gurevich, Gurevich, Maxim · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.01721

openalex publication_date 2017/11/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove a combinatorial rule for a complete decomposition, in terms of\nLanglands parameters, for representations of p-adic GL_n that appear as\nparabolic induction from a large family (ladder representations). Our rule\nobviates the need for computation of Kazhdan-Lusztig polynomials in these\ncases, and settles a conjecture posed by Lapid.\n These results are transferrable into various type A frameworks, such as the\ndecomposition of convolution products of homogeneous KLR-algebra modules, or\ntensor products of snake modules over quantum affine algebras.\n The method of proof applies a quantization of the problem into a question on\nLusztig's dual canonical basis and its embedding into a quantum shuffle\nalgebra, while computing numeric invariants which are new to the p-adic\nsetting.\n

Cited by

• Imaginary modules arising from tensor products of snake modules

Related

• On the simplicity of the tensor product of two simple modules of quantum affine algebras
• Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N)
• Polynomial families of quantum semisimple coadjoint orbits via deformed quantum enveloping algebras
• Symmetrization of representations of GL_N
• Combinatorial bases in quantum toroidal \mathfrakgl₂ modules