5 Results Found

In this article, we study the representation of generalized loop planar Galilean conformal algebra $W\left(\Gamma \right)$; we will determine the Harish-Chandra modules, Verma modules, Whittaker modules, and $U\left(h\right)$-free modules of $W\left(\Gamma \right)$.

We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective...

We survey the recent developments on quantum invariants of 3-manifolds and links: $\widehat{Z}$ and $F_L$. They are q-series invariants originated from mathematical physics, inspired by the categorification of a numerical quantum invariant—the Witten–R...

We compute the generalized noncommutative Castelnuovo-Mumford regularity of irreducible highest-weight modules over the Virasoro algebra Vir. Working over the graded negative universal enveloping algebra $A=U\left({\mathfrak{n}}_{-}\right)\subset U(Vir)$ equipped with the lev...

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux $Y(s_1,\dots ,s_k)$ with $k\ge 2$ rows—in a d-dimensional anti-de Sitter space....