Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 065, 14 pages      arXiv:1805.06971      https://doi.org/10.3842/SIGMA.2019.065
Contribution to the Special Issue on Representation Theory and Integrable Systems in honor of Vitaly Tarasov on the 60th birthday and Alexander Varchenko on the 70th birthday

Multiparameter Schur $Q$-Functions Are Solutions of the BKP Hierarchy

Natasha Rozhkovskaya
Department of Mathematics, Kansas State University, Manhattan, KS 66502, USA

Received May 20, 2019, in final form August 23, 2019; Published online August 28, 2019

Abstract
We prove that multiparameter Schur $Q$-functions, which include as specializations factorial Schur $Q$-functions and classical Schur $Q$-functions, provide solutions of the BKP hierarchy.

Key words: BKP hierarchy; symmetric functions; factorial Schur $Q$-functions; multiparameter Schur $Q$-functions; vertex operators.

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