Abstract:
The Schensted correspondence is a bijection between permutations in $S_n$ and pairs of standard Young tableaux $(P,Q)$ with $n$ boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated by a problem in cryptography, we study a graded quotient $R_n$ of the polynomial ring in $n \times n$ variables whose standard monomial theory encodes Viennot's shadow line formulation of the Schensted correspondence. The quotient ring $R_n$ may be understood as coming from the locus of permutation matrices via the machine of orbit harmonics. I will report on work of my student Moxuan Liu who has extended this theory to colored permutation groups.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974