Related papers: Once More about Spectral-Dependent Quantum $R$-Mat…
Utilizing the multiplicative formula of universal R matrix, the correspondence between the L operators and Drinfeld's generators is explicitly calculated for quantum group U_q(g) with g=A_l^{(1)}, B_l^{(1)}, C_l^{(1)}, D_l^{(1)}.
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…
The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum…
The wall-and-chamber structure of the dependence of the reductive GIT quotient on the choice of linearisation is well known. In this article, we first give a brief survey of recent results in non-reductive GIT, which apply when the…
We generalize the conformally invariant topological quantum mechanics of a particle propagating on a punctured plane by introducing a potential that breaks both the rotational and the conformal invariance down to a ${\bf Z}_2$…
This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator.…
We investigate a unitary matrix model with a complex potential with Fisher-Hartwig singularities. We show that the model exhibits finite-$N$ phase transitions. The order of the phase transition is coupling-dependent. At large-$N$, these…
We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
We study several aspects of supersymmetric models with a $U(1)_R$ symmetry where the Higgs doublet is identified with the superpartner of a lepton. We derive new, stronger bounds on the gaugino masses based on current measurements, and also…
For last two decades different quark models have predicted diverse, sometimes contradictory collections of resonant states. To choose the best among them, the obtained sets had to be compared to available experimental values. In the absence…
We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…
A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits to extract the interaction $V(\vec{r},\vec{p})$…
The classical $R$-matrix structure for the $n$-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independent $R$-matrix (without spectral parameter) when $n\ge4$. The assumption…
It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain…
We consider the ``visible'' Wigner matrix, a Wigner matrix whose $(i, j)$-th entry is coerced to zero if $i, j$ are co-prime. Using a recent result from elementary number theory on co-primality patterns in integers, we show that the…
We derive an explicit formula for the holonomy $R$-matrix of quantum $\mathfrak{sl}_2$ at a root of unity. We show it factorizes into a product of four quantum dilogarithms and satisfies a holonomy Yang-Baxter equation. This factorization…
In this paper we propose versions of the associative Yang-Baxter equation and higher order $R$-matrix identities which can be applied to quantum dynamical $R$-matrices. As is known quantum non-dynamical $R$-matrices of Baxter-Belavin type…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
Recently, we have proposed a quark mass matrix model based on U(3)$\times$U(3)$'$ family symmetry, in which up- and down-quark mass matrices $M_u$ and $M_d$ are described only by complex parameters $a_u $ and $a_d $, respectively. When we…