Naslov
Whittaker modules for $\widehat{;mathfrak {;gl};};$ and W_{;1+∞};-modules which are not tensor products
(Whittaker modules for $\widehat{;mathfrak {;gl};};$ and W_{;1+∞}; -modules which are not tensor products)

Autori
Adamović, Dražen ; Pedić Tomić, Veronika

Izvornik
Letters in Mathematical Physics (1573-0530) 113 (2023), 2; 39, 32

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Vertex algebra, Whittaker modules · W_{;1+∞}; , Typical modules

Sažetak
We consider the Whittaker modules $M_{;1}; (\bm{;\lambda};, \bm{;\mu};)$ for the Weyl vertex algebra $M$ (also called $\beta \gamma$ vertex algebra), constructed in [ALPY], where it was proved that these modules are irreducible for each finite cyclic orbifold $M^{;\Z_n};$. In this paper, we consider the modules $M_{;1};(\bm{;\lambda};, \bm{;\mu};)$ as modules for the ${;\Z};$--orbifold of $M$, denoted by $M^0$. $M^0$ is isomorphic to the vertex algebra $\mathcal W_{;1+\infty, c=-1}; = \mathcal M(2) \otimes M_1(1)$ which is the tensor product of the Heisenberg vertex algebra $M_1(1)$ and the singlet algebra $\mathcal M(2)$ (cf. \cite{;A-singlet};, \cite{;KR};, \cite{;Wa};). Furthermore, these modules are also modules of the Lie algebra $\widehat{;\mathfrak{;gl};};$ with central charge $c=-1$. We prove that they are reducible as $\widehat{;\mathfrak{;gl};};$--modules (and therefore also as $M^0$--modules), and we completely describe their irreducible quotients $L(d, \bm{;\lambda};, \bm{;\mu};)$. We show that $L(d, \bm{;\lambda};, \bm{;\mu};)$ in most cases are not tensor product modules for the vertex algebra $ \mathcal M(2) \otimes M_1(1)$. Moreover, we show that all constructed modules are typical in the sense that they are irreducible for the Heisenberg- Virasoro vertex subalgebra of $\mathcal W_{;1+\infty, c=-1};$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA