Zobrazeno 1 - 10
of 2 105
pro vyhledávání: '"Tsymbaliuk A"'
Publikováno v:
Arnold Mathematical Journal 5 (2019), no. 2, 197-283
We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these integral
Externí odkaz:
http://arxiv.org/abs/1811.12137
Autor:
Martin, Ian, Tsymbaliuk, Alexander
In this note, we construct dual PBW bases of the positive and negative subalgebras of the two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ in classical types, as used in our earlier work arXiv:2407.01450. Following the ideas of Leclerc and Clark-
Externí odkaz:
http://arxiv.org/abs/2412.06670
Autor:
Hong, Kyungtak, Tsymbaliuk, Alexander
We present a formula for trigonometric orthosymplectic $R$-matrices associated with any parity sequence. We further apply the Yang-Baxterization technique of [M.Ge, Y.Wu, K.Xue, "Explicit trigonometric Yang-Baxterization", Internat. J. Modern Phys. A
Externí odkaz:
http://arxiv.org/abs/2408.16720
Autor:
Neguţ, Andrei, Tsymbaliuk, Alexander
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 specialization maps of the corresponding shuffle algebras ([7,8,9]) in types ADE.
Externí odkaz:
http://arxiv.org/abs/2408.02411
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. 109482] to a more general class of orders on the underlying alphabet, as
Externí odkaz:
http://arxiv.org/abs/2407.19939
Autor:
Martin, Ian, Tsymbaliuk, Alexander
We construct finite $R$-matrices for the first fundamental representation $V$ of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ for classical $\mathfrak{g}$, both through the decomposition of $V\otimes V$ into irreducibles $U_{r,s}(\mathfrak{g}
Externí odkaz:
http://arxiv.org/abs/2407.01450
Publikováno v:
Zdorovʹe Rebenka, Vol 19, Iss 6, Pp 368-374 (2024)
Background. The increasing number of orphan (rare) diseases, most of which have a prevalence of less than 1 : 1,000,000, poses a serious challenge for modern medicine. In most cases, diagnosis is delayed leading to irreversible changes in the body. T
Externí odkaz:
https://doaj.org/article/7aef693684f24da4bdc835582734d585
Publikováno v:
Ukrainian Neurosurgical Journal, Iss 1, Pp 58-60 (2017)
No abstract.
Externí odkaz:
https://doaj.org/article/42c750525717423e97599927c211dd07
Autor:
Frassek, Rouven, Tsymbaliuk, Alexander
Publikováno v:
Letters in Mathematical Physics 114 (2024), Paper No. 49, 39pp
We construct Lax matrices of superoscillator type that are solutions of the RTT-relation for the rational orthosymplectic $R$-matrix, generalizing orthogonal and symplectic oscillator type Lax matrices previously constructed by the authors in arXiv:2
Externí odkaz:
http://arxiv.org/abs/2309.14199
Autor:
Avdieiev, Yehor, Tsymbaliuk, Alexander
Publikováno v:
International Mathematics Research Notices (2024), 37pp
We generalize an algorithm of Leclerc describing explicitly the bijection of Lalonde-Ram from finite to affine Lie algebras. In type $A_n^{(1)}$, we compute all affine standard Lyndon words for any order of the simple roots, and establish some proper
Externí odkaz:
http://arxiv.org/abs/2305.16299