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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.08993 |
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Table of Contents:
- We derive several identities involving Ikeda and Naruse's $K$-theoretic Schur $P$- and $Q$-functions. Our main result is a formula conjectured by Lewis and the second author which expands each $K$-theoretic Schur $Q$-function in terms of $K$-theoretic Schur $P$-functions. This formula extends to some more general identities relating the skew and dual versions of both power series. We also prove a shifted version of Yeliussizov's skew Cauchy identity for symmetric Grothendieck polynomials. Finally, we discuss some conjectural formulas for the dual $K$-theoretic Schur $P$- and $Q$-functions of Nakagawa and Naruse. We show that one such formula would imply a basis property expected of the $K$-theoretic Schur $Q$-functions.