The Bernstein-Sato b-Function of the Space of Cyclic Pairs

2014/03/03 by Walters, Robin
#14F10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1403.0633

Abstract

We compute the Bernstein-Sato polynomial of f, a function which given a pair (M,v) in X = M_n(C) × Cⁿ tests whether v is a cyclic vector for M. The proof includes a description of shift operators corresponding to the Calogero-Moser operator L_k in the rational case.

Related

• Bernstein-Sato polynomials in commutative algebra
• Introduction to a theory of b-functions
• Bernstein-Sato polynomials in positive characteristic
• Definitive Computation of Bernstein-Sato Polynomials
• Algorithms for Bernstein-Sato polynomials and multiplier ideals