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Journal of Lie Theory 28 (2018), No. 3, 673--694
Copyright Heldermann Verlag 2018

Principal Subspaces for Double Yangian DY(sl2)

Slaven Kozic
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
and: Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia


We consider the realization of level $1$ infinite-dimensional modules for the double Yangian DY$({\frak s}{\frak l}_2)$ found by K. Iohara. We use the corresponding vertex operators to generate a family of nonlocal $h$-vertex algebras $W_N$, $N\in\mathbb{Z}_{\ge0}$. Finally, we construct combinatorial bases of $W_N$ and establish a connection with the sum side of the Rogers-Ramanujan identity.

Keywords: Combinatorial basis, double Yangian, principal subspace, quantum vertex algebra.

MSC: 17B37, 17B69

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