12 papers
Chains of affine standard Lyndon words
Corbet Elkins, Alexander Tsymbaliuk
In this note, we establish the periodicity of chains of affine standard Lyndon words in all types and determine tight bounds on that periodicity, greatly generalizing the -type…
Orthosymplectic quantum groups revisited
Kyungtak Hong, Alexander Tsymbaliuk
We present the RLL-realization of extended orthosymplectic quantum supergroups for any parity sequence, with R-matrices evaluated in the earlier work arxiv:2408.16720. Our isomorph…
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…
On De Concini-Kac forms of quantum groups
Ivan Losev, Alexander Tsymbaliuk, Trung Vu
Quantum groups of semisimple Lie algebras at roots of unity admit several different forms. Among them is the De Concini-Kac form, which is the easiest to define but, perhaps, harde…
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…
Shuffle algebras and their integral forms: specialization map approach in types and
Yue Hu, Alexander Tsymbaliuk
We construct a family of PBWD bases for the positive subalgebras of quantum loop algebras of type and , as well as their Lusztig and RTT integral forms, in the new Drinf…