CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Symmetric chain decomposition of necklace posets Vivek Dhand, Michigan State University
October 4, 2011 Math 350 2-3pm	Abstract A finite ranked poset is called a symmetric chain order if it has a decomposition into rank-symmetric saturated chains. The existence of a symmetric chain decomposition is a rather strong combinatorial property which is related to the representation theory of the quantum group U_q(SL_2). Moreover, several interesting posets are conjectured to have symmetric chain decompositions. We show that if P is a symmetric chain order, then the quotient of P^n by the natural cyclic group action is also a symmetric chain order. In particular, if P is a single chain with k vertices, then the poset of n-bead k-ary necklaces is a symmetric chain order.

Symmetric chain decomposition of necklace posets

Vivek Dhand, Michigan State University

October 4, 2011

Math 350

2-3pm

Abstract

A finite ranked poset is called a symmetric chain order if it has a decomposition into rank-symmetric saturated chains. The existence of a symmetric chain decomposition is a rather strong combinatorial property which is related to the representation theory of the quantum group U_q(SL_2). Moreover, several interesting posets are conjectured to have symmetric chain decompositions. We show that if P is a symmetric chain order, then the quotient of P^n by the natural cyclic group action is also a symmetric chain order. In particular, if P is a single chain with k vertices, then the poset of n-bead k-ary necklaces is a symmetric chain order.