Related papers: Harish-Chandra modules for Yangians

These notes contain an introduction to the theory of complex semisimple quantum groups. Our main aim is to discuss the classification of irreducible Harish-Chandra modules for these quantum groups, following Joseph and Letzter. Along the…

In this note we discuss the concept of Harish-Chandra modules over the integers. The main result is a rationality result for certain intertwining operator which is used in a joint paper with Raghuram. We also discuss an interesting question…

We continue the study of Harish-Chandra bimodules in the setting of the Deligne categories $\mathrm{Rep}(G_t)$, that was started in the previous work of the first author (arXiv:2002.01555). In this work we construct a family of…

We prove a general existence result for infinite-dimensional admissible (g;k)-modules, where g is a reductive finite-dimensional complex Lie algebra and k is a reductive in g algebraic subalgebra.

We prove that any irreducible Harish-Chandra modules for a class of Lie algebras, which we call gap-$p$ Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series.These algebras are…

The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizaions of the Poisson algebra of polynomial functions on the Slodowy slice. In this…

We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain…

We construct an explicit Harish-Chandra isomorphism, from the quantum Hamiltonian reduction of the algebra D_q(GL_2) of quantum differential operators on GL_2, to the spherical double affine Hecke algebra associated to GL2. The isomorphism…

We give a classification of the Harish-Chandra modules generated by the pullback to $\text{SL}_2(\mathbb R)$ of harmonic Maass forms for congruence subgroups of $\text{SL}_2(\mathbb Z)$ with exponential growth allowed at the cusps. We…

By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin…

We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical…

The notion of a Harish-Chandra bimodule, i.e. finitely generated $U(\mathfrak{g})$-bimodule with locally finite adjoint action, was generalized to any filtered algebra in a work of Losev [Ivan Losev, Dimensions of irreducible modules over…

The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be…

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains…

We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We…

In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho)[s]$ for $s=0,\frac12$.…

A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous…

We study the Yangian $Y_n$ associated to the general linear Lie algebra $\mathfrak{gl}_n$ over a field of positive characteristic, as well as its shifted analog $Y_n(\sigma)$. Our main result gives a description of the centre of…

We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are…

Let g be a complex simple Lie algebra and h a Cartan subalgebra. The Clifford algebra C(g) of g admits a Harish-Chandra map. Kostant conjectured (as communicated to Bazlov in about 1997) that the value of this map on a (suitably chosen)…