Classical double Grothendieck transitions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912781984333824 |
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| author | Marberg, Eric |
| author_facet | Marberg, Eric |
| contents | Kirillov and Naruse have constructed double Grothendieck polynomials to represent the equivariant K-theory classes of Schubert varieties in the complete flag manifolds of types B, C, and D. We derive a recursive formula for these polynomials, extending certain K-theoretic transition equations known in type A to all classical types. As an application, we obtain an identity that expands the K-Stanley symmetric functions in types B, C, and D into positive linear combinations of K-theoretic Schur P- and Q-functions. We also resolve several positivity conjectures related to the skew generalizations of the latter functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical double Grothendieck transitions Marberg, Eric Representation Theory Combinatorics K-Theory and Homology Kirillov and Naruse have constructed double Grothendieck polynomials to represent the equivariant K-theory classes of Schubert varieties in the complete flag manifolds of types B, C, and D. We derive a recursive formula for these polynomials, extending certain K-theoretic transition equations known in type A to all classical types. As an application, we obtain an identity that expands the K-Stanley symmetric functions in types B, C, and D into positive linear combinations of K-theoretic Schur P- and Q-functions. We also resolve several positivity conjectures related to the skew generalizations of the latter functions. |
| title | Classical double Grothendieck transitions |
| topic | Representation Theory Combinatorics K-Theory and Homology |
| url | https://arxiv.org/abs/2512.19045 |