BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicolle González (UC Berkeley) DTSTART:20221129T003000Z DTEND:20221129T013000Z DTSTAMP:20260423T021225Z UID:OISTRTS/44 DESCRIPTION:Title: Higher Rank Rational (q\,t)-Catalan Polynomials and a Finite Shuffle Theo rem\nby Nicolle González (UC Berkeley) as part of OIST representation theory seminar\n\n\nAbstract\nThe classical shuffle theorem states that t he Frobenius character of the space of diagonal harmonics is given by a ce rtain combinatorial sum indexed by parking functions on square lattice pat hs. The rational shuffle theorem\, conjectured by Gorsky-Negut and proven by Mellit\, states that the geometric action on symmetric functions (descr ibed by Schiffmmann-Vasserot) of certain elliptic Hall algebra elements $P _{(m\,n)}$ yield the bigraded Frobenius character of a certain Sn represen tation. This character is known as the Hikita polynomial. In this talk I w ill introduce the higher rank rational (q\,t)-Catalan polynomials and show these are equal to finite truncations of the Hikita polynomial. By genera lizing results of Gorsky-Mazin-Vazirani and constructing an explicit bijec tion between rational semistandard parking functions and affine compositio ns\, I will derive a finite analog of the rational shuffle theorem in the context of spherical double affine Hecke algebras.\n LOCATION:https://researchseminars.org/talk/OISTRTS/44/ END:VEVENT END:VCALENDAR