H. Yamane

activity

19962026

most citedDrinfeld second realization of the quantum affine superalgebras of

D^{(1)} (2, 1; x)

via the Weyl groupoid

31 citations · 81 across the 20 of their papers we have counts for

collaborators

22 papers

math.QA2026

Universal $R$ -matrix of double parameter quantum affine algebra $U_{q, Q} (s l_{2}^)$

Fengchang Li, Masatake Maruyama, Hiroyuki Yamane

We give the explicit formula of the universal $R$ -matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type $A_{1}^{(1)}$ . For $N$ …

math.QA2021

Hamilton circuits of Cayley graphs of Weyl groupoids of generalized quantum groups

Hiroyuki Yamane

We study Hamilton circuits of the Cayley graphs of the Weyl groupoids of the generalized quantum groups, or the quantum double of the Nichols algebras of diagonal-type, with finite…

math.QA2019

Typical Irreducible Characters of Generalized Quantum Groups

Hiroyuki Yamane

We introduce the definition of the typical irreducible modules of the generalized quantum groups, and prove the Weyl-Kac-type formulas of their characters. As a by-product, we obta…

math.QA2019★ 1 cited

Natural Elements of Center of Generalized Quantum Groups

Punita Batra, Hiroyuki Yamane

This paper gives elements in the (skew) center of the generalized quantum group corresponding to its irreducible finite dimensional modules. Finally we give a conjecture stating th…

math.QA2018

Lowest positive almost central elements of $U_{q} (s l^{(1)} (n ∣ n))$ $(n \geq 2)$ , $U_{q} (s l^{(2)} (2 n ∣2 n))$ $(n \geq 2)$ and $U_{q} (s l^{(4)} (2 n + 1∣2 n + 1))$ $(n \geq 1)$ and their multi-parameter quantum affine superalgebras

Hiroyuki Yamane

Let $π : s l (n ∣ n) \to A (n - 1, n - 1)$ be the natural epimorphism of Lie superalgebra. Then $dim ker π = 1$ . Let $π^{(t)} : s l^{(t)} (n ∣ n) \to A^{(t)} (n - 1, n - 1)$ be the natural epimorphism, where…

math.QA2017★ 3 cited

Kostant-Lusztig $A$ -bases of Multiparameter Quantum Groups

Naihuan Jing, Kailash Misra, Hiroyuki Yamane

We study the Kostant-Lusztig $A$ -base of the multiparameter quantum groups. To simplify calculations, especially for $G_{2}$ -type, we utilize the duality of the pairing of th…

Universal R-matrix of double parameter quantum affine algebra Uq,Q​(sl2​^​)

Hamilton circuits of Cayley graphs of Weyl groupoids of generalized quantum groups

Typical Irreducible Characters of Generalized Quantum Groups

Natural Elements of Center of Generalized Quantum Groups

Lowest positive almost central elements of Uq​(sl(1)(n∣n)) (n≥2), Uq​(sl(2)(2n∣2n)) (n≥2) and Uq​(sl(4)(2n+1∣2n+1)) (n≥1) and their multi-parameter quantum affine superalgebras

Kostant-Lusztig A-bases of Multiparameter Quantum Groups

Universal $R$ -matrix of double parameter quantum affine algebra $U_{q, Q} (s l_{2}^)$

Lowest positive almost central elements of $U_{q} (s l^{(1)} (n ∣ n))$ $(n \geq 2)$ , $U_{q} (s l^{(2)} (2 n ∣2 n))$ $(n \geq 2)$ and $U_{q} (s l^{(4)} (2 n + 1∣2 n + 1))$ $(n \geq 1)$ and their multi-parameter quantum affine superalgebras

Kostant-Lusztig $A$ -bases of Multiparameter Quantum Groups