Related papers: Matrix coefficients of intertwining operators and …

According to the work of Berkovits, Vafa and Witten (hep-th/9902098), the non-linear sigma model on the supergroup PSU(1,1|2) is the essential building block for string theory on AdS(3)xS(3)xT(4). Models associated with a non-vanishing…

Let u and v be permutations on n letters, with u <= v in Bruhat order. A Bruhat interval polytope Q_{u,v} is the convex hull of all permutation vectors z = (z(1), z(2),...,z(n)) with u <= z <= v. Note that when u=e and v=w_0 are the…

Consider a random graph $G$ of size $N$ constructed according to a \textit{graphon} $w \, : \, [0,1]^{2} \mapsto [0,1]$ as follows. First embed $N$ vertices $V = \{v_1, v_2, \ldots, v_N\}$ into the interval $[0,1]$, then for each $i < j$…

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is…

We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large enough indices. We show how this ring $\tilde{\Lambda}$ is…

It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice…

Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…

We introduce a class of generalized universal irrational rotation $C^*$-algebras $A_{\theta,\gamma}=C^*(x,w)$ which is characterized by the relations $w^*w=ww^*=1$, $x^*x=\gamma(w)$, $xx^*=\gamma(e^{-2\pi i\theta}w)$, and $xw=e^{-2\pi…

Let $q = e^{i \theta} \in \mathbb{T}$ (where $\theta \in \mathbb{R}$), and let $u,v$ be $q$-commuting unitaries, i.e., $u$ and $v$ are unitaries such that $vu = quv$. In this paper we find the optimal constant $c = c_\theta$ such that $u,v$…

Let $V$ be a vertex operator algebra and $A^{\infty}(V)$ and $A^{N}(V)$ for $N\in \mathbb{N}$ the associative algebras introduced by the author in [H5]. For a lower-bounded generalized $V$-module $W$, we give $W$ a structure of graded…

The integral formulae pertaining to the unitary group $\mathsf{U}(d)$ have been comprehensively reviewed, yielding fresh results and innovative proofs. Central to the derivation of these formulae lies the employment of Schur-Weyl duality, a…

For each finite, irreducible Coxeter system $(W,S)$, Lusztig has associated a set of "unipotent characters" $\Uch(W)$. There is also a notion of a "Fourier transform" on the space of functions $\Uch(W) \to \RR$, due to Lusztig for Weyl…

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…

Let $R$ be an associative ring with unity $1$ and consider that $2,k$ and $2k\in \mathbb{N}$ are invertible in $R$. For $m\geq 1$ denote by $UT_n(m,R)$ and $UT_{\infty}(m,R)$, the subgroups of $UT_n(R)$ and $UT_{\infty}(R)$ respectively,…

For links $L \subset \Sigma \times [0,1]$, where $\Sigma$ is a closed orientable surface, we define a $U_q(\mathfrak{gl}(1|1))$ Reshetikhin-Turaev invariant with coefficients in $\mathbb{Z}[H_1(\Sigma)]$. This invariant turns out to be…

In arXiv:0707.2151 the authors introduced the theory of local representations of the quantum Teichm\"uller space $\mathcal{T}^q_S$ ($q$ being a fixed primitive $N$-th root of $(-1)^{N + 1}$) and they studied the behaviour of the…

We discuss non-compact WZW sigma models, especially the ones with symmetric space $H^{\bf C}/H$ as the target, for $H$ a compact Lie group. They offer examples of non-rational conformal field theories. We remind their relation to the…

Let $H^{\infty}(E)$ be the Hardy algebra of a $W^{*}$-correspondence $E$ over a $W^{*}$-algebra $M$. Then the ultraweakly continuous completely contractive representations of $H^{\infty}(E)$ are parametrized by certain sets…

We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody group $G$ (affine or not) over a nonarchimedean local field $K$. It has a canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a…