Related papers: RSK correspondence for King tableaux with Berele i…
A recent paper \cite{KMMO} introduced the stochastic U_q(A_n^{(1)}) vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group U_q(A_n^{(1)}) by a gauge transformation. We will show that a certain function…
A coplactic class in the symmetric group S_n consists of all permutations in S_n with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of S_n which is…
We investigate Robinson-Schensted-Knuth algorithm (RSK) and Sch\"utzenberger's jeu de taquin in the infinite setup. We show that the recording tableau in RSK defines an isomorphism of the following two dynamical systems: (i) a sequence of…
The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay law. The Wigner-Weisskopf survival amplitude,…
We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or…
In this paper, we explore the relationship between quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions. We introduce a bijection on $\mathsf{SPIT}(\alpha)$ such that $\{\mathrm{w}_{\rm c}(T) \mid T \in…
Let $q$ be a $2N$th root of unity where $N$ is odd. Let $U_q(sl_2)$ denote the quantum group with large center corresponding to the lie algebra $sl_2$ with generators $E,F,K$, and $K^{-1}$. A semicyclic representation of $U_q(sl_2)$ is an…
We apply the strategy to study of diffeomorphisms via block diffeomorphisms to the world of positive scalar curvature (psc) metrics. For each closed psc manifold $M$, we construct the cubical set $\widetilde{\mathcal{R}^{+}_{\bullet}}(M)$…
Lascoux has given a triangular version of the Cauchy identity where Schur polynomials are replaced by Demazure characters and Demazure atoms. He has then used the staircase expansion to recover expansions for all Ferrers shapes, where the…
We introduce a new semantic communication mechanism - SemanticRL, whose key idea is to preserve the semantic information instead of strictly securing the bit-level precision. Unlike previous methods that mainly concentrate on the network or…
We derive a renormalized classical spin (RCS) theory for $S > 1/2$ quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP$^1$ phase space of dipolar SU($2$) coherent states.…
This paper provides a construction of the unipotent representations for classical complex groups in terms of the Theta correspondence as introduced and studied by R. Howe. The K-type structure of unipotent representations is obtained as a…
We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf{c},\mathbf{s}}$ corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras. To this end we give unified…
We present a general framework connecting global symmetries to the relativistic $S$-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize…
Semantic communication initiates a new direction for future communication. In this paper, we aim to establish a systematic framework of semantic information theory (SIT). First, we propose a semantic communication model and define the…
We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape…
We discuss various features and details of two versions of the Barrett-Crane spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian model and second of the SL(2,C)-symmetric Lorentzian version in which all tetrahedra…
We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X.…
The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of $p$-adic reductive groups. We describe generalizations to arbitrary such representations of several results recently obtained in the…
An involution in a Coxeter group has an associated set of involution words, a variation on reduced words. These words are saturated chains in a partial order first considered by Richardson and Springer in their study of symmetric varieties.…