Schubert puzzles and integrability I: invariant trilinear forms
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2017
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918122222518272 |
|---|---|
| author | Knutson, Allen Zinn-Justin, Paul |
| author_facet | Knutson, Allen Zinn-Justin, Paul |
| contents | The puzzle rules for computing Schubert calculus on $d$-step flag manifolds, proven in [Knutson Tao 2003] for $1$-step, in [Buch Kresch Purbhoo Tamvakis 2016] for $2$-step, and conjectured in [Coskun Vakil 2009] for $3$-step, lead to vector configurations (one vector for each puzzle edge label) that we recognize as the weights of some minuscule representations. The $R$-matrices of those representations (which, for $2$-step flag manifolds, involve triality of $D_4$) degenerate to give us puzzle formulae for two previously unsolved Schubert calculus problems: $K_T(2$-step flag manifolds$)$ and $K(3$-step flag manifolds$)$. The $K(3$-step flag manifolds$)$ formula, which involves 151 new puzzle pieces, implies Buch's correction to the first author's 1999 conjecture for $H^*(3$-step flag manifolds$)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_10019 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Schubert puzzles and integrability I: invariant trilinear forms Knutson, Allen Zinn-Justin, Paul Combinatorics Mathematical Physics Algebraic Geometry The puzzle rules for computing Schubert calculus on $d$-step flag manifolds, proven in [Knutson Tao 2003] for $1$-step, in [Buch Kresch Purbhoo Tamvakis 2016] for $2$-step, and conjectured in [Coskun Vakil 2009] for $3$-step, lead to vector configurations (one vector for each puzzle edge label) that we recognize as the weights of some minuscule representations. The $R$-matrices of those representations (which, for $2$-step flag manifolds, involve triality of $D_4$) degenerate to give us puzzle formulae for two previously unsolved Schubert calculus problems: $K_T(2$-step flag manifolds$)$ and $K(3$-step flag manifolds$)$. The $K(3$-step flag manifolds$)$ formula, which involves 151 new puzzle pieces, implies Buch's correction to the first author's 1999 conjecture for $H^*(3$-step flag manifolds$)$. |
| title | Schubert puzzles and integrability I: invariant trilinear forms |
| topic | Combinatorics Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/1706.10019 |