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LLT Polynomials and Schur Positivity in Rational Shuffle Conjecture
Algebra & Discrete Mathematics| Speaker: | Mikhail Mazin, KSU |
| Related Webpage: | https://www.math.ksu.edu/~mmazin |
| Location: | 1147 MSB |
| Start time: | Fri, Sep 11 2015, 2:10PM |
Description
Rational Shuffle conjecture provides a combinatorial formula
in
terms of rational parking functions for certain symmetric polynomials,
naturally appearing in the theory of Macdonald polynomials and K-theory
of
Hilbert schemes. These polynomials are believed to be Schur positive. In
this talk I will discuss our recent result, showing that the
combinatorial
side of the rational Shuffle conjecture is indeed Schur positive. The
proof
is based on comparing the contributions of parking functions with a
fixed
underlying Dyck path with LLT polynomials, which are known to be Schur
positive.
The talk is based on a joint work with Eugene Gorsky.