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SUMMARY:Tianyuan Xu (University of Colorado Boulder)
DTSTART:20200925T170000Z
DTEND:20200925T174000Z
DTSTAMP:20260423T004038Z
UID:SheRepTh/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SheRepTh/4/"
 >On Kazhdan-Lusztig cells of a-value 2</a>\nby Tianyuan Xu (University of 
 Colorado Boulder) as part of Sherbrooke Meeting on Representation Theory o
 f Algebras\, Corona Edition (fully online)\n\n\nAbstract\nLusztig's a-func
 tion on a Coxeter group $W$ is a function that takes\n\n\n\na constant non
 negative integer value on each Kazhdan--Lusztig cell of $W$.  The\nfunctio
 n plays a key role in the study of the cells of $W$ and the cell\nrepresen
 tations of the Hecke algebra of $W$\, but it is also very difficult to\nco
 mpute. For an element $w \\in W$\, it is known that $a(w)=0$ if and\nonly 
 if $W$ is the identity and $a(w)=1$ if and only if $w$ has a\nunique nonem
 pty reduced word\; moreover\, the elements of $a$-values $0$\nand $1$ each
  form a single two-sided cell. We report on some extensions of these\nresu
 lts about the set $W_2$ of elements with $a$-value $2$. In particular\,\nw
 e classify Coxeter groups $W$ where $W_2$ is finite\, count $W_2$ and desc
 ribe\nthe partition of $W_2$ into cells when $W_2$ is finite\, and discuss
  a\nconnection between cell representations associated to $W_2$ and the re
 flection\nrepresentation of $W$ in types ADE. (Joint work with Richard Gre
 en.)\n
LOCATION:https://researchseminars.org/talk/SheRepTh/4/
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