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Events for May – September 2011

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Aug. 30, 2011 2pm (MATH 350)	Lie Theory Fred Goodman (Iowa) X The Birman--Murakami--Wenzl algebra (or BMW algebra for short) plays an important role in knot theoretic invariants and in centralizer algebras for quantum groups. It may be defined either by (rather complicated) generators and relations, or as an algebra of diagrams with a pictorially defined multiplication. Affine and cyclotomic Hecke algebras are related to the Hecke algebras of type A in the same way that the wreath products Z \wr S_n and (Z/rZ) \wr S_n are related to the symmetric group S_n. The affine and cyclotomic BMW algebras discussed in this talk are BMW analogues of affine and cyclotomic Hecke algebras. Affine and cyclotomic BMW algebras
Sep. 06, 2011 2pm (MATH 350)	Lie Theory Richard Green (CU) X A problem in algebraic geometry is to compute Schubert intersection numbers. These count the points of intersection of generically translated Schubert varieties. For minuscule flag varieties such as Grassmannians, these numbers can be computed by a combinatorial rule called "jeu de taquin", which in the Grassmannian case is called the Littlewood--Richardson rule. This talk will describe this combinatorial rule and some of its key properties. No knowledge of algebraic geometry will be assumed. Generalized Littlewood--Richardson rules
Sep. 13, 2011 2pm (MATH 350)	Lie Theory Tyson Gern (CU) X Kazhdan--Lusztig polynomials arise in the context of Hecke algebras associated to Coxeter groups. The computation of these polynomials is very difficult for examples of even moderate rank. It known that the leading coefficients, \mu(x,w) all 0 or 1 when x is fully commutative in type A, but in type D there are certain "bad" elements that make \mu value computation difficult. I will investigate a projection of the Kazhdan--Lusztig basis of the Hecke algebra with the goal of computing \mu values involving these "bad" elements. A Projection of the Kazhdan--Lusztig Basis in Type D I
Sep. 20, 2011 2pm (MATH 350)	Lie Theory Tyson Gern (CU) X Kazhdan--Lusztig polynomials arise in the context of Hecke algebras associated to Coxeter groups. The computation of these polynomials is very difficult for examples of even moderate rank. It known that the leading coefficients, \mu(x,w) all 0 or 1 when x is fully commutative in type A, but in type D there are certain "bad" elements that make \mu value computation difficult. I will investigate a projection of the Kazhdan--Lusztig basis of the Hecke algebra with the goal of computing \mu values involving these "bad" elements. A Projection of the Kazhdan--Lusztig Basis in Type D II
Sep. 27, 2011 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X The Hopf algebra of symmetric functions in noncommuting variables NCSym(X) has an representation theoretic realization as a space of supercharacters of the finite unipotent upper-triangular matrices. In such a correspondence, the representation theory gives several distinguished sets of bases for NCSym(X). However, it is also natural to ask whether we learn anything about supercharacters from such a correspondence. This talk gives one possible answer to such a question, demonstrating how an obvious basis of NCSym(X) has a surprising representation theoretic interpretation on supercharacters. This is joint work with N. Bergeron. Symmetric functions and the representation theory of unipotent upper-triangular matrices

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