Filtrations and recursions for Schubert modules
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911551606226944 |
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| author | Anderson, David |
| author_facet | Anderson, David |
| contents | Revisiting Kraśkiewicz and Pragacz's construction of Schubert modules, we provide a new proof that their characters are equal to Schubert polynomials. The main innovation is a representation-theoretic interpretation of a recurrence relation for Schubert polynomials recently discovered by Nadeau, Spink, and Tewari. Along the way, we review several related constructions, and show that the Nadeau-Spink-Tewari recursion determines the characters of flagged Schur modules coming from the broader classes of "transparent" and "translucent" diagrams. We conclude with a conjecture concerning the Schubert positivity of the characters of transparent diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filtrations and recursions for Schubert modules Anderson, David Combinatorics Representation Theory Revisiting Kraśkiewicz and Pragacz's construction of Schubert modules, we provide a new proof that their characters are equal to Schubert polynomials. The main innovation is a representation-theoretic interpretation of a recurrence relation for Schubert polynomials recently discovered by Nadeau, Spink, and Tewari. Along the way, we review several related constructions, and show that the Nadeau-Spink-Tewari recursion determines the characters of flagged Schur modules coming from the broader classes of "transparent" and "translucent" diagrams. We conclude with a conjecture concerning the Schubert positivity of the characters of transparent diagrams. |
| title | Filtrations and recursions for Schubert modules |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2408.16694 |