Date

2013

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Mathematics

First Adviser

Skandera, Mark

Other advisers/committee members

Isaak, Garth; Szczepanski, Susan; Greene, Curtis

Abstract

Combinatorial interpretations have been used to show the total nonnegativity of induced trivial character and induced sign character immanants. The irreducible character immanants are known to be totally nonnegative as well, however, providing a combinatorial interpretation remains an open problem. To find such combinatorial interpretations we explore the quantum analogs of the symmetric group characters associated to the above mentioned immanants. In this paper, a combinatorial interpretation for the quantum induced sign characters on certain elements of the Hecke algebra is provided. This interpretation is then related to the quantum chromatic symmetric function introduced by Shareshian and Wachs. These interpretations involve a certain class of posets and associated planar networks. Lastly, for a restricted subset of these planar networks, properties of the sequence of coefficients of the induced sign characters of the Hecke algebra are discussed.

Included in

Mathematics Commons

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