Related papers: $\beta$-WLZZ models from $\beta$-ensemble integral…
We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of…
The notion of the Drazin inverse of an even-order tensor with the Einstein product was introduced, very recently [J. Ji and Y. Wei. Comput. Math. Appl., 75(9), (2018), pp. 3402-3413]. In this article, we further elaborate this theory by…
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and…
The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices. We present a self-contained proof of the Fourier transform formula for this distribution. Our method…
The WZW models describe the dynamics of the edge modes of Chern-Simons theories in three dimensions. We explore the WZW models which can be mapped to supersymmetric theories via the generalized Jordan-Wigner transformation. Some of such…
In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having…
We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is…
In this work, we begin to uncover the architecture of the general family of zeta functions and multiple zeta values as they appear in the theory of integrable systems and conformal field theory. One of the key steps in this process is to…
Since the ($\beta$-deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of ${\mathfrak{gl}}(1)$. In this paper, we construct two general cases of the $\beta$-deformed Hurwitz Kontsevich model. We find that…
We present the exact realization of the extended Snyder model. Using similarity transformations, we construct realizations of the original Snyder and the extended Snyder models. Finally, we present the exact new realization of the…
We use zesting and symmetry gauging of modular tensor categories to analyze some previously unrealized modular data obtained by Grossman and Izumi. In one case we find all realizations and in the other we determine the form of possible…
We show that the CFT with symmetry group $G_{k_1}\times G_{k_2}\times \cdots \times G_{k_n}$ consisting of WZW models based on the same group $G$, but at arbitrary integer levels, admits an integrable deformation depending on $2(n-1)$…
We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally…
We introduce the first random matrix model of a complex $\beta$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys.,…
We suggest an invariant way to enumerate nodal and nodal-cuspidal real deformations of real plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version…
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index.…
We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p- adic group, indexed by the Weyl group. We show that the elements of this basis may be…
Wandzura-Wilczek (WW) relations between matrix-elements of bilocal light-ray operators have recently regained interest in connection with off-forward scattering processes. Originally derived for matrix elements over leading-twist operators,…
There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function,…