Doctor of Philosophy
Other advisers/committee members
Isaak, Garth; Szczepanski, Susan; Greene, Curtis
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.
Shelton, Brittany Colleen, "Combinatorial Interpretations of Induced Sign Characters of the Hecke Algebra" (2013). Theses and Dissertations. 1622.