Fourier matrices for $G(d,1,n)$ from quantum general linear groups

DOI10.1016/J.JALGEBRA.2021.06.034arXiv2011.11332MaRDI QIDQ6354328

Publication date: 23 November 2020

Abstract: We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group

G (d, 1, n)

. The construction of the category follows the decomposition of the Fourier matrix as a Kronecker tensor product of exterior powers of the character table

S

of the cyclic group of order

d

. The representation of the quantum universal enveloping algebra of the general linear Lie algebra

m a t h f r a k {g l}_{m}

, with quantum parameter an even root of unity of order

2 d

, provides a categorical interpretation of the matrix

. We also prove some positivity conjectures of Cuntz at the decategorified level.

Mathematics Subject Classification ID

Group theory and generalizations (20-XX) Associative rings and algebras (16-XX)

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