135 citations · 516 across the 43 of their papers we have counts for
5 papers · 2 filters
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 in classical types, as used in our ea…
Orthosymplectic -matrices
Kyungtak Hong, Alexander Tsymbaliuk
We present a formula for trigonometric orthosymplectic -matrices associated with any parity sequence, and establish their factorization into the ordered product of -exponents…
Fusion and specialization for type ADE shuffle algebras
Andrei Neguţ, Alexander Tsymbaliuk
Root vectors in quantum groups (of finite type) generalize to fused currents in quantum loop groups ([5]). In the present paper, we construct fused currents as duals to specializat…
Standard Lyndon loop words: weighted orders
Severyn Khomych, Nazar Korniichuk, Kostiantyn Molokanov +1
We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109…
Two-Parameter Quantum Groups and -Matrices: Classical Types
Ian Martin, Alexander Tsymbaliuk
We construct finite -matrices for the first fundamental representation of two-parameter quantum groups for classical , both through the…