Discrete CATS Seminar
UNIVERSITY OF KENTUCKY
DISCRETE CATS SEMINAR
WHERE CATS = COMBINATORICS, ALGEBRA, TOPOLOGY AND STATISTICS!
112 PATTERSON OFFICE TOWER
MASTERS EXAM TALK
"Some Aspects of Groups Acting on Finite Posets"
University of Kentucky
Tuesday, April 15, 2008
9:30 am, 205 Classroom Building
Let P be a finite poset (partially ordered set) and G a subgroup of
the full group of automorphisms of P. The action of G on P defines
linear representations of G. We present a representation and two
examples in detail. In the symmetric group S_n acting on the Boolean
algebra B_n, the multiplicity of the irreducible representation lambda
in the virtual representation beta_S is equal to the number of
standard Young tableaux of shape lambda and descent set S. In the
case of the symmetric group S_n acting on the lattice of partitions of
an n-set, we find an analogous description of beta_S.