Decomposition numbers of the cyclotomic Brauer algebra over the complex field, II

2025/02/04 by Rui, Hebing, Song, Linliang
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.02081

Abstract

Following Nazarov's suggestion, the cyclotomic Nazarov-Wenzl algebra is referred to as the cyclotomic Brauer algebra. This paper focuses on computing the decomposition numbers of the cyclotomic Brauer algebra over ℂ with arbitrary parameters. We show that these decomposition numbers can be expressed in terms of the parabolic Kazhdan-Lusztig polynomials of type D_n, with a parabolic subgroup of type A, under Condition 1.2.

Related

• Decomposition numbers of cyclotomic Brauer algebras over the complex field, I
• Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero
• Koszul gradings on Brauer algebras
• Cyclotomic Nazarov-Wenzl algebras
• Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra