A $t$-generalization for Schubert Representatives of the Affine Grassmannian
We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$. The families are defined by a statistic on combinatorial objects associated to the type-$A$ affine Weyl group an...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2371/pdf |
| _version_ | 1797270264995643392 |
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| author | Avinash J. Dalal Jennifer Morse |
| author_facet | Avinash J. Dalal Jennifer Morse |
| author_sort | Avinash J. Dalal |
| collection | DOAJ |
| description | We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$. The families are defined by a statistic on combinatorial objects associated to the type-$A$ affine Weyl group and their transition matrix with Hall-Littlewood polynomials is $t$-positive. We conjecture that one family is the set of $k$-atoms. |
| first_indexed | 2024-04-25T02:01:31Z |
| format | Article |
| id | doaj.art-2c26b47133c94653ba2039a98e69fccd |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:31Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-2c26b47133c94653ba2039a98e69fccd2024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23712371A $t$-generalization for Schubert Representatives of the Affine GrassmannianAvinash J. Dalal0Jennifer Morse1Department of mathematics [Philadelphie]Department of mathematics [Philadelphie]We introduce two families of symmetric functions with an extra parameter $t$ that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when $t=1$. The families are defined by a statistic on combinatorial objects associated to the type-$A$ affine Weyl group and their transition matrix with Hall-Littlewood polynomials is $t$-positive. We conjecture that one family is the set of $k$-atoms.https://dmtcs.episciences.org/2371/pdf$k$-schur functionspieri rulebruhat orderhall-littlewood polynomials[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Avinash J. Dalal Jennifer Morse A $t$-generalization for Schubert Representatives of the Affine Grassmannian Discrete Mathematics & Theoretical Computer Science $k$-schur functions pieri rule bruhat order hall-littlewood polynomials [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | A $t$-generalization for Schubert Representatives of the Affine Grassmannian |
| title_full | A $t$-generalization for Schubert Representatives of the Affine Grassmannian |
| title_fullStr | A $t$-generalization for Schubert Representatives of the Affine Grassmannian |
| title_full_unstemmed | A $t$-generalization for Schubert Representatives of the Affine Grassmannian |
| title_short | A $t$-generalization for Schubert Representatives of the Affine Grassmannian |
| title_sort | t generalization for schubert representatives of the affine grassmannian |
| topic | $k$-schur functions pieri rule bruhat order hall-littlewood polynomials [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2371/pdf |
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