Naslov
Vertex operators and principal subspaces of level one for Uq(sl^2)

Autori
Kožić, Slaven

Izvornik
Journal of algebra (0021-8693) 455 (2016); 251-290

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

Ključne riječi
affine lie algebra ; quantum affine algebra ; quantum vertex algebra ; principal subspace ; quasi-particle ; combinatorial basis

Sažetak
We consider two different methods of associating vertex algebraic structures with the level 1 principal subspaces for Uq(slˆ2). In the first approach, we introduce certain commutative operators and study the corresponding vertex algebra and its module. We find combinatorial bases for these objects and show that they coincide with the principal subspace bases found by B.L. Feigin and A.V. Stoyanovsky. In the second approach, we introduce the, so-called nonlocal q-vertex algebras, investigate their properties and construct the nonlocal q-vertex algebra and its module, generated by Frenkel–Jing operator and Koyama's operator respectively. By finding the combinatorial bases of their suitably defined subspaces, we establish a connection with the sum sides of the Rogers–Ramanujan identities. Finally, we discuss further applications to quantum quasi-particle relations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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