Related papers: Identities in the Superintegrable Chiral Potts Mod…

In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…

We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.

The purpose of this paper is to give symmetric identities for higher-order degenerate q- Bernoulli polynomials arising from the p-adic q-integral on Zp.

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1…

We define a new class of integrable vertex models associated to quantum groups at roots of unit

We identify the quantum group ${\Large\textsl{U}}_\textsl{w}(sl_2)$ in the $L$-operator of $\tau^{(2)}$-model for a generic $\textsl{w}$ as a subalgebra of $U_{\sf q} (sl_2)$ with $\textsl{w} = {\sf q}^{-2}$. In the roots of unity case,…

We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We…

The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to…

In this paper we derive new identities satisfied by Chebyshev polynomials of the first kind and big q-Jacobi polynomials. An immediate benefit of the derived identities is the achievement of closed-form expressions for the Laurent…

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.

We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the…

Monopole operators play a central role in 3 dimensional supersymmetric dualities: a careful understanding of their spectrum is necessary to match chiral operators on either sides of a conjectured duality. In Chern-Simons theories…

Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…

We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the…

We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.

It is shown that in large symmetrical nanoparticles additional quantum numbers are required to label unambiguously symmetry adapted linear combinations of the wave functions. It is obtained that the labels of irreducible representations…

In this paper we construct new categorical models for the identity types of Martin-L\"of type theory, in the categories Top of topological spaces and SSet of simplicial sets. We do so building on earlier work of Awodey and Warren, which has…

Incorporating its most relevant global symmetry, chiral effective models are aimed at investigating, in a simplified framework, important aspects of the yet unsolved QCD. We review some recent results obtained in these models on the…

We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…