arXiv subjects

Hyohe Miyachi

Publications and source records attributed to Hyohe Miyachi.

5 recordsLinked to original sources

arXiv2018

On the Mackey formulas for cyclotomic Hecke algebras and categories O of rational Cherednik algebras

In this paper, we shall establish the Mackey formulas in the following two set ups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of parabolic subgroups. (ii) on the Bezrukavnikov-Etingof induction and restriction functors among categories O of rational Cherednik algebras for the complex reflection group of type G(r, 1, n) and their parabolic subgroups.

math.RT↗

arXiv2016

Parallelotope tilings and $q$-decomposition numbers

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of $U_q(\widehat{\mathfrak{sl}}_e)$. These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the $\mathrm{Ext}^1$-quivers of $v$-Schur algebras at complex $e$-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the $1$-skeletons of the polytopal complexes.

math.RT↗

arXiv2011

Decomposition matrices for $d$-Harish-Chandra series: the exceptional rank two cases

We calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank 2 exceptional complex reflection groups in characteristic 0. We prove the existence of canonical basic sets in the sense of Geck-Rouquier and show that all modular irreducible representations can be lifted to the ordinary ones.

math.RT↗

arXiv2003

Constructible characters and canonical bases

We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of $U_v(sl_\infty)$. These formulas coincide at v=1 with Lusztig's formulas for the constructible characters of the Iwahori-Hecke algebras of type B and D.

math.QA↗

arXiv2001

Some closed formulas for canonical bases of Fock spaces

We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of U_v(sl^_n). As a result, a combinatorial description of certain parabolic Kazhdan-Lusztig polynomials for affine type A is obtained.

math.QA↗