Lie algebras generated by reflections in types BCD

2025/06/01 by Drupieski, Christopher M., Kujawa, Jonathan R. · 1 citation
#17B60 #20F55 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.01198

Abstract

We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of even-signed permutations), viewed as Lie algebras via the commutator bracket, and determine the structure of the Lie subalgebras generated by the sets of reflections.

Citations

• The Lie superalgebra of transpositions
• Image of the Artin groups of classical types inside the finite Iwahori-Hecke algebras
• Image of the braid groups inside the finite Iwahori-Hecke algebras
• On Kottwitz' conjecture for twisted involutions
• On the representation theory of braid groups

Cited by

• Lie Superalgebras Generated by Reflections in Weyl Groups of Classical Type

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