# METROPLEX AGANT SEMINAR

### (Algebraic Geometry, Algebra and Number Theory Seminar)

a joint venture of UNT, UTA and TCU

*``A Generalization of the Iwahori-Hecke Algebra''*

**Abstract:** The Iwahori-Hecke algebras of Coxeter groups play a
central role in the study of representations of semisimple Lie-type groups.
An important tool is the combinatorial approach to representations of
Iwahori-Hecke algebras introduced by Kazhdan and Lusztig in 1979. In this
talk, we will discuss a generalization of the Iwahori-Hecke algebra of the
symmetric group that is instead based on the complex reflection group
*G(r,1,n)*. Using the analogues of Kazhdan and Lusztig's
*R*-polynomials, we will show that our algebra determines a partial
order on *G(r,1,n)* that generalizes the Chevalley-Bruhat order on the
symmetric group. We will also consider possible analogues of
Kazhdan-Lusztig polynomials.
No prior knowledge of any of the terms used in the last paragraph will be
assumed. [In fact, the talk may be viewed as a quick introduction to some
of the central ideas in Kazhdan-Lusztig theory.] The talk should be
accessible to all graduate students who have taken, or are currently taking,
a beginning graduate algebra course.

Please mention/email this talk to any interested parties
and to your students if you are teaching an advanced undergraduate algebra
class or a graduate algebra class.

Note that on the same day, there will be a colloquium at UTA at 2 pm of
interest to algebraists and geometers. Please see
http://www.uta.edu/math/pages/main/seminar.htm#colloquium
for more info.
^{1}Driving & Parking (Revised Jan 12, 2006)

If you are travelling from out of town, then a map of UTA may be found at
http://www.uta.edu/maps/. Note that
PKH is the triangular building in the central-campus region of the map.
Click on central campus to zoom in, & PKH is in the SE corner of that
submap, next to the "garage" & is on Nedderman Drive between College St
(aka Planatarium Place) & West St.
West St is one-way northbound between W Mitchell St & 3rd St. Parking
is available in the nearby (East & SE of PKH) parking lots with a UTA
permit (but many people park there late on Fridays with no permit & are
not caught). There are a few metered parking spots on the East side of
Pickard Hall on West St. Visitor (free), & metered, parking is available
by Davis Hall (marked DH in SW part of the submap). A parking garage
(expensive) is nextdoor to PKH (use West St to get to it). Note that if
heading south on Cooper, then no left turn is allowed to Nedderman Dr.
Recommended route from UNT: eventually head south on Hwy 360 (or Industrial
Blvd = Collins), West on Abram, south (left) on Center, West (right) on
W Mitchell. Then use map. Alternatively, get to I30 heading East, & follow
directions from TCU given below. From TCU: east on I30, exit Cooper, South
on Cooper, left (East) on W Mitchell, then use map. (Note that Nedderman
Drive between West St & Pecan St is permanently closed.)

Note that PKH 487 is on the 4th floor of PKH; turn right out of elevator
on 4th floor.

Questions, etc on arrangements/directions? Contact Michaela Vancliff. Please notify
us if coming from out of town, since, if you are a little late, we will
delay the start of the talk for you.