Actions of the quantum toroidal algebra of type sl2 on the space of vertex operators for Uq(gl2) modules.

Authors :: Kei Miki
Source :: Journal of Mathematical Physics; 2016, Vol. 57 Issue 7, p1-17, 17p
Publication Year :: 2016
Abstract: Highest weight modules for U<subscript>q</subscript>(gl<subscript>2</subscript>) are endowed with a structure of modules for the quantum toriodal algebra U<subscript>κ</subscript> of type sl<subscript>2</subscript>. Using this, we define U<subscript>κ</subscript> actions on the space of vertex operators for irreducible highest weight U<subscript>q</subscript>(gl<subscript>2</subscript>) modules. Highest or lowest weight vectors of the thus obtained U<subscript>κ</subscript> modules are expressed in terms of an intertwiner for U<subscript>q</subscript>(sl<subscript>2</subscript>) modules and an extra boson. The submodules generated by these vectors are investigated. [ABSTRACT FROM AUTHOR]

Subjects :: VERTEX operator algebras
MODULES (Algebra)
VECTORS (Calculus)
BOSONS
QUANTUM theory
MODULE structure in Banach spaces
TOROIDAL harmonics
QUANTUM algebra

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