Discrete CATS Seminar
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UNIVERSITY OF KENTUCKY **

DISCRETE CATS SEMINAR

WHERE CATS = COMBINATORICS, ALGEBRA, TOPOLOGY AND STATISTICS!

112 PATTERSON OFFICE TOWER

SPRING 2008

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MASTERS EXAM TALK

"Some Aspects of Groups Acting on Finite Posets"

JiYoon Jung

University of Kentucky

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Tuesday, April 15, 2008

9:30 am, 205 Classroom Building

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Abstract:

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.