**NB:** A PDF
version of this announcement (suitable for posting) is also available.
# Hecke algebras of type B and Markov traces

### Rosa Orellana

University of California, San Diego

###
February 1, 1999

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
The Hecke algebras of type $A$ arise naturally in the study of knot
theory, quantum groups, and Von Neumann algebras. Their relation to
the symmetric and braid groups allows for their study using
combinatorics and low dimensional topology.

In this talk I will define the Hecke algebras of type $A$ and $B$ and
show their relation to the symmetric group and the braid group (this
groups will be defined in this talk). I will also construct a
beautiful homomorphism from a specialization of the Hecke algebra of
type $B$ onto a reduced Hecke algebra of type $A$. I will show how
this homomorphism can be used to compute some traces on the Hecke
algebra of type $B$, called Markov traces. If time permits, I will
give other applications of this homomorphism.

This talk will be accessible to graduate students.