Journal of Lie Theory

no. 3
Principal Subspaces for Double Yangian DY(sl2)
Slaven Kozic1, 2
1School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
2Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 673-694
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.
DOI: 10.5802/jolt.1020
Classification: 17B37, 17B69
Keywords: Combinatorial basis, double Yangian, principal subspace, quantum vertex algebra

Slaven Kozic  1 , 2

1 School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
2 Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia 
Slaven Kozic. Principal Subspaces for Double Yangian DY(sl2). Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 673-694. doi: 10.5802/jolt.1020
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     author = {Slaven Kozic},
     title = {Principal {Subspaces} for {Double} {Yangian} {DY(sl\protect\textsubscript{2})}},
     journal = {Journal of Lie Theory},
     pages = {673--694},
     year = {2018},
     volume = {28},
     number = {3},
     doi = {10.5802/jolt.1020},
     zbl = {1422.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1020/}
}
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