Related papers: A Nekrasov-Okounkov type formula for type C

This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the $GL_n$ case in [CR22]. In the context of the type $CC_n$ affine root system the Macdonald polynomials of other root systems…

We study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of generalized Macdonald polynomials, derive the loop…

We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$,…

We postulate a supplemental power counting within the heavy quark effective theory, that results in a small, highly-constrained set of second-order power corrections, compared to the standard approach. We determine all $\bar{B} \to D^{(*)}$…

In 2010, G.-N. Han obtained the generating function for the number of size $t$ hooks among integer partitions. Here we obtain these generating functions for self-conjugate partitions, which are particularly elegant for even $t$. If…

The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used…

In arXiv:1106.4305 extended superpolynomials were introduced for the torus links T[m,mk+r], which are functions on the entire space of time variables and, at expense of reducing the topological invariance, possess additional algebraic…

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…

This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of…

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…

We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the…

Davydov-Yetter cohomology classifies infinitesimal deformations of tensor categories and of tensor functors. Our first result is that Davydov-Yetter cohomology for finite tensor categories is equivalent to the cohomology of a comonad…

We introduce a new criterion which tests if a given decomposition of a given ternary form $T$ of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points $Z$ associated to the…

We study $t$-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra $A_1^{(1)}$. We obtain closed form formulas for certain $t$-string functions of levels 2 and 4. As corollaries, we obtain…

The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the…

Starting from some linear algebraic data (a Weyl-group invariant bilinear form) and some arithmetic data (a bilinear Steinberg symbol), we construct a cover of a Kac-Moody group generalizing the work of Matsumoto. Specializing our…

We construct families of Newton-Okounkov bodies for the free group character varieties and configuration spaces of any connected reductive group. We use this construction to give a proof that these spaces are Cohen-Macaulay.

We investigate the $\Lambda_c \to \Lambda \ell^{+} \nu_\ell$ decay with a focus on potential new physics (NP) effects in the $\ell = \mu$ channel. We employ an effective Hamiltonian within the framework of the Standard Model Effective Field…

Given a presentably symmetric monoidal $\infty$-category $\mathcal{C}$ and an $\mathbb{E}_{\infty}$-monoid $M$, we introduce and classify twisted graded categories, which generalize the Day convolution structure on $\mathrm{Fun}(M,…

In this paper, we study linear codes over $\mathbb{Z}_k$ based on lattices and theta functions. We obtain the complete weight enumerators MacWilliams identity and the symmetrized weight enumerators MacWilliams identity based on the theory…