Related papers: Howe duality and dynamical Weyl group

We provide an explicit expression for the modular hamiltonian of the von Neumann algebras associated to the unit double cone for the (fermionic) quantum field theories of the 2-component Weyl (helicity 1/2) field, and of the 4-component…

We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by non-trivial background fields interacting with both fermions and…

Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and…

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…

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 utilize a theorem of B. Feigin and S. Loktev to give explicit bases for the global Weyl modules for the map algebras of the form $\mathfrak{sl}_n\otimes A$ of highest weight $m\omega_1$. These bases are given in terms of specific…

Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…

We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a $k$-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of $F_{\mu\nu}F^{\mu\nu}$. We…

We consider the rational dynamical quantum group $E_y(gl_2)$ and introduce an $E_y(gl_2)$-module structure on $\oplus_{k=0}^n H^*_{GL_n\times\C^\times}(T^*Gr(k,n))'$, where $H^*_{GL_n\times\C^\times}(T^*Gr(k,n))'$ is the equivariant…

We point out that for N=4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with…

A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space $\mathcal{H}$ and an involutive unitary $R$-Matrix $S$ is studied. This algebra carries a natural vacuum state, and the corresponding Fock…

We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…

The partition algebra $\mathsf{P}_k(n)$ and the symmetric group $\mathsf{S}_n$ are in Schur-Weyl duality on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the permutation module $\mathsf{M}_n$ of $\mathsf{S}_n$, so there is a…

We prove a `motivic' analogue of the Weyl character formula, computing the Euler characteristic of a line bundle on a generalized flag manifold $G/B$ multiplied either by a motivic Chern class of a Schubert cell, or a Segre analogue of it.…

The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine Lie algebra and the second one is a new…

In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and Weyl-Heisenberg group on the two-torus are constructed.…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

We study the relation between $\mathcal{W}_{1+\infty}$ algebra and Arbesfeld-Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of…

We use chain level genus zero Gromov-Witten theory to associate to any closed monotone symplectic manifold a formal group (loosely interpreted), whose Lie algebra is the odd degree cohomology of the manifold (with vanishing bracket). When…

We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie…