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Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Thursday, July 15, 14:35 ~ 15:10 UTC-3

Theta operators, Macdonald polynomials, and new symmetric function operator identities

Marino Romero

University of California, San Diego, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Theta operators are symmetric function operators that were first introduced by D'Adderio, Iraci and Wyngaerd in order to give the Delta Conjecture a compositional refinement. It was then also conjectured that the Frobenius characteristic of the space of coinvariants in two sets of commuting and two sets of anticommuting variables can be given using the Theta operators (extending a conjecture of Zabrocki). We will present several new symmetric function operator identities that can be specialized to give Theta operator identities. In turn, many identities in the literature regarding Delta eigenoperators of the modified Macdonald basis become consequences of our identities. We will also discuss two of the main tools used in proving our identities: Tesler's Identity and Garsia-Mellit's Five Term Relation, two fundamental identities in the theory of modified Macdonald polynomials. Part of our presentation is based off joint work with Michele D'Adderio.

Joint work with Michele D'Adderio (Université Libre de Bruxelles).

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