Related papers: Shuffle algebras, lattice paths and Macdonald func…

The classical algebra $\Lambda$ of symmetric functions has a remarkable deformation $\Lambda^*$, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a distinguished basis formed by shifted Schur…

We introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions $\lambda$ and…

Writing the values of Krawtchouk polynomials as matrices, we consider weighted partial sums along columns. For the general case, we find an identity that, in the symmetric case yields a formula for such partial sums. Complete sums of…

We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery (LS) representations within the surface code. Our approach employs the ZX calculus to establish an equivalence between…

We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this…

We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large…

This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion…

We define and study the shuffle algebra $Sh_{m|n}$ of the quantum toroidal algebra $\mathcal E_{m|n}$ associated to Lie superalgebra $\mathfrak{gl}_{m|n}$. We show that $Sh_{m|n}$ contains a family of commutative subalgebras $\mathcal…

We introduce a new family of symmetric functions, which are $q$-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine…

We introduce new families of cylindric symmetric functions as subcoalgebras in the ring of symmetric functions $\Lambda$ (viewed as a Hopf algebra) which have non-negative structure constants. Combinatorially these cylindric symmetric…

We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a…

We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time…

We study Wilson loop expectations in lattice Yang-Mills models with a compact Lie group $G$. Using tools recently introduced in a companion paper, we provide alternate derivations, interpretations, and generalizations of several recent…

In "Self-adjoint Operators as Functions I: Lattices, Galois Connections, and the Spectral Order" [arXiv:1208.4724], it was shown that self-adjoint operators affiliated with a von Neumann algebra N can equivalently be described as certain…

Suppose $M$ and $N$ are positive integers and let $k = \gcd(M, N)$, $m = M/k$, and $n=N/k$. We define a symmetric function $L_{M,N}$ as a weighted sum over certain tuples of lattice paths. We show that $L_{M,N}$ satisfies a generalization…

We obtain explicit formulas for the $1$-point functions of all states in the symmetrized Heisenberg algebra $M^+$ and symmetrized lattice VOAs $V_L^+$. For this we employ a new $\mathbf Z_2$-twisted variant of so-called Zhu recursion.

We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $\beta= 2N/g^{2}$. Our method makes…

We construct a new class of operators that act on symmetric functions with two deformation parameters $q$ and $t$. Our combinatorial construction associates each operator with a specific lattice path, whose steps alternate between moving up…

The partition function of the W_N minimal model CFT is computed in the large N 't Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the…

Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix. Then the skew-Borel decomposition $ m_{\iy}:= Q^{-1} J…