135 citations · 516 across the 43 of their papers we have counts for
44 papers
Scary Wheels (and Super Shrubs)
Andrei Neguţ, Alexander Tsymbaliuk
We prove the shuffle realization for quantum affine superalgebras of types in the loop realization, in that we construct an isomorphism between each of these algebras and a…
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…
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…
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…
Affine standard Lyndon words
Corbet Elkins, Alexander Tsymbaliuk
In this note, we establish the convexity and monotonicity for affine standard Lyndon words in all types, generalizing the -type results of arXiv:2305.16299. We also derive parti…
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…
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…
Orthosymplectic Yangians
Rouven Frassek, Alexander Tsymbaliuk
We study the RTT orthosymplectic super Yangians and present their Drinfeld realizations for any parity sequence, generalizing the results for non-super types BCD, a standard parity…
Orthosymplectic superoscillator Lax matrices
Rouven Frassek, Alexander Tsymbaliuk
We construct Lax matrices of superoscillator type that are solutions of the RTT-relation for the rational orthosymplectic -matrix, generalizing orthogonal and symplectic oscilla…
Affine Standard Lyndon words: A-type
Yehor Avdieiev, Alexander Tsymbaliuk
We generalize an algorithm of Leclerc describing explicitly the bijection of Lalonde-Ram from finite to affine Lie algebras. In type , we compute all affine standard Lyn…
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 (for type only) integral f…
A first test of CUPID prototypal light detectors with NTD-Ge sensors in a pulse-tube cryostat
CUPID collaboration, K. Alfonso, A. Armatol +176
CUPID is a next-generation bolometric experiment aiming at searching for neutrinoless double-beta decay with ~250 kg of isotopic mass of Mo. It will operate at 10 mK…
Twelve-crystal prototype of LiMoO scintillating bolometers for CUPID and CROSS experiments
CUPID, CROSS collaborations, : +182
An array of twelve 0.28 kg lithium molybdate (LMO) low-temperature bolometers equipped with 16 bolometric Ge light detectors, aiming at optimization of detector structure for CROSS…
Shuffle approach towards quantum affine and toroidal algebras
Alexander Tsymbaliuk
These are detailed lecture notes of the crash-course on shuffle algebras delivered by the author at Tokyo University of Marine Science and Technology during the second week of Marc…
Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems
Alexander Tsymbaliuk
We present a shuffle realization of the GKLO-type homomorphisms for shifted quantum affine, toroidal, and quiver algebras, thus generalizing its rational version of arXiv:2104.1451…
Toward CUPID-1T
A. Armatol, C. Augier, F. T. Avignone +172
Current experiments to search for broken lepton-number symmetry through the observation of neutrinoless double-beta decay () provide the most stringent limits on the…
Optimization of the first CUPID detector module
CUPID collaboration, A. Armatol, C. Augier +175
CUPID will be a next generation experiment searching for the neutrinoless double decay, whose discovery would establish the Majorana nature of the neutrino. Based on the experi…
Transfer matrices of rational spin chains via novel BGG-type resolutions
Rouven Frassek, Ivan Karpov, Alexander Tsymbaliuk
We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras , whose highest weight is a multiple…
Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
Rouven Frassek, Alexander Tsymbaliuk
Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of rational Lax matrices, polynomial in the spectral param…