The PBW basis of $U_{q,\bar{q}}(\ddot{\mathfrak{gl}}_n)$

Andrei Negu\c{t}

The PBW basis of $U_{q,\bar{q}}(\ddot{\mathfrak{gl}}_n)$

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arxiv 1905.06277 v3 pith:5OXST5Q2 submitted 2019-05-15 math.QA math.COmath.RT

Andrei Neguţ This is my paper · ORCID

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keywords algebrabasisquantumtoroidaltypeakinauthorburban-schiffmann

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We consider the PBW basis of the type A quantum toroidal algebra developed by the author, and prove commutation relations between its generators akin to the ones studied by Burban-Schiffmann for n=1. This gives rise to a new presentation of the quantum toroidal algebra of type A.

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A tale of two shuffle algebras
math.QA 2019-08 conditional novelty 8.0 of 10

New shuffle algebra presentations of the top and bottom halves of U_{q,q}(gl_n) yield a topological coproduct extending the Drinfeld-Jimbo coproduct on the horizontal subalgebra.

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