Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Hiraku Abe"'
Publikováno v:
Journal of Combinatorics. 10:27-59
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73fffab09cfcea0e8912dbf930d24936
https://doi.org/10.4310/joc.2019.v10.n1.a2
https://doi.org/10.4310/joc.2019.v10.n1.a2
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a toric variety. We give a complete classification of Fano and weak Fano re
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::25b5392db12c0d34fb65bfc290aec842
http://arxiv.org/abs/2003.12286
http://arxiv.org/abs/2003.12286
Autor:
Hiraku Abe, Tatsuya Horiguchi
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9789811574504
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In particular, we will see how hyperplane arrangements, representations of symmetric groups, and Stanley
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::de60979f437d43f36b65989e59bf4c14
https://doi.org/10.1007/978-981-15-7451-1_10
https://doi.org/10.1007/978-981-15-7451-1_10
Publikováno v:
International Mathematics Research Notices. 2019:5316-5388
Let $n$ be a fixed positive integer and $h: \{1,2,\ldots,n\} \rightarrow \{1,2,\ldots,n\}$ a Hessenberg function. The main results of this paper are two-fold. First, we give a systematic method, depending in a simple manner on the Hessenberg function
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f6d8535f5d9bc7ee7b267f4d276efa6f
https://doi.org/10.1093/imrn/rnx275
https://doi.org/10.1093/imrn/rnx275
Autor:
Tatsuya Horiguchi, Hiraku Abe
Publikováno v:
Topology and its Applications. 208:143-159
The Springer variety of type $A$ associated to a nilpotent operator on $\mathbb{C}^n$ in Jordan canonical form admits a natural action of the $\ell$-dimensional torus $T^{\ell}$ where $\ell$ is the number of the Jordan blocks. We give a presentation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1d4704fa5cf2cc08b3f51c86a893991
https://doi.org/10.1016/j.topol.2016.05.004
https://doi.org/10.1016/j.topol.2016.05.004
Autor:
Hiraku Abe, Sara Billey
Publikováno v:
Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016)
In 1990, Lakshmibai and Sandhya published a characterization of singular Schubert varieties in flag manifolds using the notion of pattern avoidance. This was the first time pattern avoidance was used to characterize geometrical properties of Schubert
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d161df7d2d6f62d9281ece0cc5b45b4e
https://doi.org/10.2969/aspm/07110001
https://doi.org/10.2969/aspm/07110001
Autor:
Peter Crooks, Hiraku Abe
This work is intended to contextualize and enhance certain well-studied relationships between Hessenberg varieties and the Toda lattice, thereby building on the results of Kostant, Peterson, and others. One such relationship is the fact that every La
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::20df55e2a8e3febbe6781f8739d62446
Autor:
Tomoo Matsumura, Hiraku Abe
Publikováno v:
Journal of Algebraic Combinatorics. 42:875-892
In this paper, we introduce a family of symmetric polynomials by specializing the factorial Schur polynomials. These polynomials represent the weighted Schubert classes of the cohomology of the weighted Grassmannian introduced by Corti-Reid, and we r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a003777752fc62ccb3809937a11c0d3
https://doi.org/10.1007/s10801-015-0608-z
https://doi.org/10.1007/s10801-015-0608-z
Let $\mathfrak{g}$ be a complex semisimple Lie algebra. For a regular element $x$ in $\mathfrak{g}$ and a Hessenberg space $H\subseteq \mathfrak{g}$, we consider a regular Hessenberg variety $X(x,H)$ in the flag variety associated with $\mathfrak{g}$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de48d6f199a88fc3c3d2540275ce7f6e
http://arxiv.org/abs/1712.09269
http://arxiv.org/abs/1712.09269