Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras Uq(sun) corresponding to Lie algebras of the groups SUn, taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-...

Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras Uq(sun) corresponding to Lie algebras of the groups SUn, taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-...

We establish the \(Q {\widetilde{Q}}\)-systems for twisted quantum affine algebras that were conjectured in Frenkel and Hernandez (Commun Math Phys 362(2):361–414, 2018). develop representation theory of Borel subalgebra we construct their prefundamental representations. also propose a general conjecture on relations between non-twisted types. prove this some particular classes representations,...

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint ⊗ adjoint → adjoint. We present a practical method for the determination of these quantum...

We study of the category O for the queer Lie superalgebra q(n), and the corresponding block decomposition induced by infinitesimal central characters. In particular, we show that the so-called typical blocks correspond to standardly stratified algebras, in the sense of Cline, Parshall and Scott. By standard arguments for Lie algebras, modified to the superalgebra situation, we prove that these ...

We present an elementary approach in characterizing Lie polynomials the generators $A,B$ of algebra with a defining relation that is form deformed or twisted commutation $AB=\sigma(BA)$ where deformation twisting map $\sigma$ linear polynomial slope parameter not root unity. The class algebras defined as such encompasses $q$-deformed Heisenberg algebras, rotation and some types $q$-oscillator w...

In this paper, we introduce the notions of (∈,∈ ∨ q)-N -ideals and (γ, δ)-N -ideals of subtraction algebras, which are generalization of N -ideals. Some characterization for these generalized N -ideals are derived. Also, we introduce the notions of (∈,∈ ∨ q)-N -ideals and N -ideals with thresholds of subtraction algebras. The characterization of N -ideals with thresholds by their closed (f, t)-...

We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras defined over fields of characteristic zero are now known in...