Alternating Subalgebras of Hecke Algebras and Alternating Subgroups of Braid Groups

Abstract

For a Coxeter system (G, S) the multi-parametric alternating subalgebra H ⁺(G) of the Hecke algebra and the alternating subgroup ℬ⁺(G) of the braid group are defined. Two presentations for H ⁺(G) and ℬ⁺(G) are given; one generalizes the Bourbaki presentation for the alternating subgroups of Coxeter groups, another one uses generators related to edges of the Coxeter graph.

Key Words:

• Alternating subalgebras
• Alternating subgroups
• Braid groups
• Coxeter graph
• Coxeter groups
• Hecke algebras

2010 Mathematics Subject Classification:

• 20F05
• 20F36
• 16S80

ACKNOWLEDGMENT

We thank I. Marin for useful discussions. First author on leave of absence from P. N. Lebedev Physical Institute, Moscow, Russia.

Notes

Communicated by S. Sehgal.