|Date: Friday, March 23, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Odd symmetric functions
Abstract: We introduce the odd symmetric functions, a Z-graded Hopf superalgebra which exhibits signed analogues of many of the combinatorial properties of the classical symmetric functions: elementary and complete bases, Kostka numbers, Schur functions, RSK and Littlewood-Richardson, and so forth. This superalgebra is obtained as a quotient of a q-Hopf algebra isomorphic to the graded dual of the quantum quasi-symmetric functions. It also arises as the kernel of odd divided difference operators which act on skew polynomials; these operators are part of an odd nilHecke algebra. Odd nilHecke algebras can be used to categorify half of quantum sl(2) and, conjecturally, give a 2-representation theoretic construction of odd Khovanov homology.
Speaker: Alexander Ellis
Institution: Columbia University