A. Hoshino

activity

20042021

most citedA commutative algebra on degenerate CP^1 and Macdonald polynomials

129 citations · 200 across the 10 of their papers we have counts for

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7 papers · 1 filter

math.QA2021

Branching Formula for $q$ -Toda Function of Type B

Ayumu Hoshino, Yusuke Ohkubo, Jun'ichi Shiraishi

We present a proof of the explicit formula for the asymptotically free eigenfunctions of the $B_{N}$ $q$ -Toda operator which was conjectured by the first and third authors. This form…

math.QA2020★ 3 cited

Branching Rules for Koornwinder Polynomials with One Column Diagrams and Matrix Inversions

Ayumu Hoshino, Jun'ichi Shiraishi

We present an explicit formula for the transition matrix $C$ from the type $B C_{n}$ Koornwinder polynomials $P_{(1^{r})} (x ∣ a, b, c, d ∣ q, t)$ with one column diagrams, to the type…

math.QA2018★ 2 cited

Macdonald Polynomials of Type $C_{n}$ with One-Column Diagrams and Deformed Catalan Numbers

Ayumu Hoshino, Jun'ichi Shiraishi

We present an explicit formula for the transition matrix $C$ from the type $C_{n}$ degeneration of the Koornwinder polynomials $P_{(1^{r})} (x ∣ a, - a, c, - c ∣ q, t)$ with one…

math.QA2010★ 40 cited

Kernel function and quantum algebras

B. Feigin, A. Hoshino, J. Shibahara +2

We introduce an analogue $K_{n} (x, z; q, t)$ of the Cauchy-type kernel function for the Macdonald polynomials, being constructed in the tensor product of the ring of symmetric functions…

math.QA2005★ 22 cited

Polyhedral Realizations of Crystal Bases for Quantum Algebras of Finite Types

Ayumu Hoshino

Polyhedral realization of crystal bases is one of the methods for describing the crystal base $B (\infty)$ explicitly. This method can be applied to symmetrizable Kac-Moody types. W…

math.QA2004★ 1 cited

Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Arbitrary Rank 2 Cases