UIUC Dept. of Mathematics Seminar Calendar

     August 2008           September 2008          October 2008    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                 1  2       1  2  3  4  5  6             1  2  3  4
  3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
 10 11 12 13 14 15 16   14 15 16 17 18 19 20   12 13 14 15 16 17 18
 17 18 19 20 21 22 23   21 22 23 24 25 26 27   19 20 21 22 23 24 25
 24 25 26 27 28 29 30   28 29 30               26 27 28 29 30 31   
 31

Wednesday, September 17, 2008

Algebra, Geometry and Combinatorics Seminar
3:00 pm in Altgeld Hall 345, Wednesday, September 17, 2008

Del

Edit

Copy

Submitted by ayong.

Rinat Kedem (Department of Mathematics, University of Illinois)
Finite dimensional representations of quantum affine algebrasand cluster algebras
Abstract: There is a subset of finite-dimensional quantum affine algebra modules which seems to have a particularly simple description. In the case of g=A_n, they are analogues of modules with "rectangular highest weights". The (q)-characters of these modules satisfy a closed system of recursion relations. These are discrete integrable systems or discrete Hirota equations in special cases. As a result one can write fermionic formulas for their characters. One can also reformulate the category as a cluster algebra, to help prove such formulas. I will explain these words, as well as the general picture about how several different theorems fit into it.