Odd symmetric functions and categorification
 Title:
 Odd symmetric functions and categorification
 Author(s):
 Ellis, Alexander Palen
 Thesis Advisor(s):
 Khovanov, Mikhail G.
 Date:
 2013
 Type:
 Dissertations
 Department(s):
 Mathematics
 Persistent URL:
 http://hdl.handle.net/10022/AC:P:20307
 Notes:
 Ph.D., Columbia University.
 Abstract:
 We introduce q and signed analogues of several constructions in and around the theory of symmetric functions. The most basic of these is the Hopf superalgebra of odd symmetric functions. This algebra is neither (super)commutative nor (super)cocommutative, yet its combinatorics still exhibit many of the striking integrality and positivity properties of the usual symmetric functions. In particular, we give odd analogues of Schur functions, Kostka numbers, and LittlewoodRichardson coefficients. Using an odd analogue of the nilHecke algebra, we give a categorification of the integral divided powers form of U_q^+(sl_2) inequivalent to the one due to KhovanovLauda. Along the way, we develop a graphical calculus for indecomposable modules for the odd nilHecke algebra.
 Subject(s):
 Mathematics
 Item views
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 Metadata:

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 Suggested Citation:
 Alexander Palen Ellis, 2013, Odd symmetric functions and categorification, Columbia University Academic Commons, http://hdl.handle.net/10022/AC:P:20307.