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You searched for +publisher:"U of Massachusetts : PhD" +contributor:("Julianna Tymoczko"). One record found.

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1. Koonz, Jennifer. Properties of Singular Schubert Varieties.

Degree: PhD, Mathematics, 2013, U of Massachusetts : PhD

This thesis deals with the study of Schubert varieties, which are subsets of flag varieties indexed by elements of Weyl groups. We start by defining Lascoux elements in the Hecke algebra, and showing that they coincide with the Kazhdan-Lusztig basis elements in certain cases. We then construct a resolution (<em>Zw, π</em>) of the Schubert variety Xw for which <em>Rπ*(C[l(w)])</em> is a sheaf on Xw whose expression in the Hecke algebra is closely related to the Lascoux element. We also define two new polynomials which coincide with the intersection cohomology Poincar\'e polynomial in certain cases. In the final chapter, we discuss some interesting combinatorial results concerning Bell and Catalan numbers which arose throughout the course of this work. Advisors/Committee Members: Eric Sommers, Tom Braden, Julianna Tymoczko.

Subjects/Keywords: Combinatorics; Hecke Algebra; Intersection Cohomology; Kazhdan-Lusztig Polynomials; Schubert Varieties; Mathematics

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APA (6th Edition):

Koonz, J. (2013). Properties of Singular Schubert Varieties. (Doctoral Dissertation). U of Massachusetts : PhD. Retrieved from https://scholarworks.umass.edu/open_access_dissertations/839

Chicago Manual of Style (16th Edition):

Koonz, Jennifer. “Properties of Singular Schubert Varieties.” 2013. Doctoral Dissertation, U of Massachusetts : PhD. Accessed November 27, 2020. https://scholarworks.umass.edu/open_access_dissertations/839.

MLA Handbook (7th Edition):

Koonz, Jennifer. “Properties of Singular Schubert Varieties.” 2013. Web. 27 Nov 2020.

Vancouver:

Koonz J. Properties of Singular Schubert Varieties. [Internet] [Doctoral dissertation]. U of Massachusetts : PhD; 2013. [cited 2020 Nov 27]. Available from: https://scholarworks.umass.edu/open_access_dissertations/839.

Council of Science Editors:

Koonz J. Properties of Singular Schubert Varieties. [Doctoral Dissertation]. U of Massachusetts : PhD; 2013. Available from: https://scholarworks.umass.edu/open_access_dissertations/839

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