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We study the effect of diagram automorphisms on rank-level duality. We use it to prove new symplectic rank-level dualities on genus zero smooth curves with marked points and chosen coordinates. We also show that rank-level dualities for the…

We study the spectrum of confining strings in SU(3) pure gauge theory, by means of lattice Monte Carlo simulations, using torelon operators in different representations of the gauge group. Our results provide direct evidence that the string…

We consider the group theoretical properties of R--R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra $\IG_s\subset U$ of the U--duality algebra that generates the scalar…

Let $G$ be a simple graph with $n$ vertices and $e(G)$ edges, and $q_1(G)\geq q_2(G)\geq\cdots\geq q_n(G)\geq0$ be the signless Laplacian eigenvalues of $G.$ Let $S_k^+(G)=\sum_{i=1}^{k}q_i(G),$ where $k=1, 2, \ldots, n.$ F. Ashraf et al.…

We prove a collection of $q$-series identities conjectured by Warnaar and Zudilin and appearing in recent work with H. Kim in the context of superconformal field theory. Our proof utilizes a deformation of the simple affine vertex operator…

Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…

For the simple Lie algebra $ \frak{so}_m$, we study the commutant vertex operator algebra of $ L_{\hat{\frak{so}}_{m}}(n,0)$ in the $n$-fold tensor product $ L_{\hat{\frak{so}}_{m}}(1,0)^{\otimes n}$. It turns out that this commutant vertex…

Let $S_2^*(q)$ be the set of primitive Hecke eigenforms of weight 2 and prime level $q$. For $p$ prime and $t\in \mathbb{R}$, we prove asymptotic formulas for the sums $$ \mathcal {A}(p^j,q,t)=\sum_{f\in S_2^*(q)}…

This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space $L(X)$ of an oriented differentiable stack $X$ and show…

We show that with high probability the random graph $G_{n, 1/2}$ has an induced subgraph of linear size, all of whose degrees are congruent to $r\pmod q$ for any fixed $r$ and $q\geq 2$. More generally, the same is true for any fixed…

We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…

A well known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking…

Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this…

Trigonometric formulas are derived for certain families of associated Legendre functions of fractional degree and order, for use in approximation theory. These functions are algebraic, and when viewed as Gauss hypergeometric functions,…

In this paper we construct a Lie algebra representation of the algebraic string bracket on negative cyclic cohomology of an associative algebra with appropriate duality. This is a generalized algebraic version of the main theorem of [AZ]…

We show that the complex hypergeometric function describing $6j$-symbols for $SL(2,\mathbb{C})$ group is a special degeneration of the $V$-function -- an elliptic analogue of the Euler-Gauss $_2F_1$ hypergeometric function. For this…

This paper aims to study the low dimensional cohomology of Hom-Lie algebras and q-deformed W(2,2) algebra. We show that the q-deformed W(2,2) algebra is a Hom-Lie algebra. Also, we establish a one-to-one correspondence between the…

In this paper it is shown that the one-dimensional configuration sums of the solvable lattice models of Andrews, Baxter and Forrester and the string functions associated with admissible representations of the affine Lie algebra A$_1^{(1)}$…

We prove the refined Loughran--Smeets conjecture of Loughran--Rome--Sofos for a wide class of varieties arising as products of conic bundles. One interesting feature of our varieties is that the subordinate Brauer group may be arbitrarily…

We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…