Orthogonal basis for the Shapovalov form on A_n

2012/06/16 by Andrey Mudrov, Mudrov, Andrey
Mathematics · Physics and Astronomy · #17B37 #22E47 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:22E47 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1206.3647

25 pages, no figures. Lemma 9.1 corrected

openalex publication_date 2012/06/16 · arxiv created 2014/08/31 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U be either classical or quantized universal enveloping algebra of \sł(n+1) extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in U over the extended Cartan subalgebra diagonalizing the contravariant Shapovalov form on generic Verma module. The matrix coefficients of the form are calculated and the inverse of the form is explicitly constructed.

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