A. H. Morales, I. Pak, G. Panova, “Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials”, Zap. Nauchn. Sem. POMI, 2021, Volume 507,Pages <nobr>59

Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials

A. H. Morales^a, I. Pak^b, G. Panova^c

^a Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA
^b Department of Mathematics, University of California, Los Angeles, CA 90095, USA
^c Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Abstract: We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes, our formulas generalize the classical hook-length formula and the Littlewood formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its $q$-analogs, which were studied in previous papers of the series.

Key words and phrases: hook-length formula, factorial symmetric functions, Grothendieck polynomials, standard Young tableaux, increasing tableaux.

UDC: 519.112

Received: 29.08.2021

Language: English