Ian Martin

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math.RT2025

Orthogonal bases for two-parameter quantum groups

Ian Martin, Alexander Tsymbaliuk

In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups $U_{r, s} (g)$ in classical types, as used in our ea…

math.RT2025

Bicharacter twists of quantum groups

Ian Martin, Alexander Tsymbaliuk

We apply the general construction of a twist of bigraded Hopf algebras by skew bicharacters to obtain two-parameter quantum groups in the Drinfeld-Jimbo, new Drinfeld (for affine t…

math.RT2025

Two-Parameter Quantum Groups and $R$ -Matrices: Classical Types

Ian Martin, Alexander Tsymbaliuk

We construct finite $R$ -matrices for the first fundamental representation $V$ of two-parameter quantum groups $U_{r, s} (g)$ for classical $g$ , both through the…

Orthogonal bases for two-parameter quantum groups

Bicharacter twists of quantum groups

Two-Parameter Quantum Groups and R-Matrices: Classical Types

Two-Parameter Quantum Groups and $R$ -Matrices: Classical Types