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pro vyhledávání: '"Masuda, Mikiya"'
A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the full flag variety $\mathrm{Fl}(\mathbb{C}^n)$ associated with a regular semisimple matrix $S$ of order $n$ and a function $h$ from $\{1,2,\dots,n\}$ to itself
Externí odkaz:
http://arxiv.org/abs/2405.16399
Foata and Sch\"{u}tzenberger gave an expansion for the Eulerian polynomial $A_n(t)$ in terms of the basis $\{t^j(1+t)^{n-1-2j}\}$ for the space of polynomials $f(t)$ satisfying $f(t)=t^{n-1}f(1/t)$. We generalize this result in two ways. First, we pr
Externí odkaz:
http://arxiv.org/abs/2405.09242
A flag variety is a homogenous variety $G/B$ where $G$ is a simple algebraic group over the complex numbers and $B$ is a Boel subgroup of $G$. A Schubert variety $X_w$ is a subvariety of $G/B$ indexed by an element $w$ in the Weyl group of $G$. It is
Externí odkaz:
http://arxiv.org/abs/2311.11535
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot acti
Externí odkaz:
http://arxiv.org/abs/2310.16235
The $c_1$-cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a $c_1$-preserving isomorphism between their integral cohomology rings. In this paper, we confirm the conjecture for smoot
Externí odkaz:
http://arxiv.org/abs/2310.03219
Autor:
Masuda, Mikiya, Sato, Takashi
A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the flag variety determined by a square matrix $S$ with distinct eigenvalues and a Hessenberg function $h$. The cohomology ring $H^*(\mathrm{Hess}(S,h))$ is indepe
Externí odkaz:
http://arxiv.org/abs/2301.03762
Autor:
Masuda, Mikiya, Sato, Takashi
The solution of Shareshian-Wachs conjecture by Brosnan-Chow linked together the cohomology of regular semisimple Hessenberg varieties and graded chromatic symmetric functions on unit interval graphs. On the other hand, it is known that unicellular LL
Externí odkaz:
http://arxiv.org/abs/2205.15526
The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand--Serganova in the mid-1980s, but it seems that not much has been done since then. In this chapter, we present some of the work by Klyachko and Gelf
Externí odkaz:
http://arxiv.org/abs/2203.16750
We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple Hessenberg variety becomes a module of a symmetric group $\mathfrak{S}_
Externí odkaz:
http://arxiv.org/abs/2203.11580
For an equivariantly formal action of a compact torus $T$ on a smooth manifold $X$ with isolated fixed points we investigate the global homological properties of the graded poset $S(X)$ of face submanifolds. We prove that the condition of $j$-indepen
Externí odkaz:
http://arxiv.org/abs/2203.10641