Heisenberg-Type Families in $U_q(\widehat{sl_2})$
Alexander Zuevsky
TL;DR
This paper introduces a new family of Heisenberg-type elements within the quantum affine algebra $U_q(\\widehat{sl_2})$, providing explicit formulas and exploring their algebraic properties.
Contribution
It constructs and explicitly describes a novel family of Heisenberg-type elements in $U_q(\widehat{sl_2})$ using the second Drinfeld realization.
Findings
Defined a new family of Heisenberg-type elements
Derived explicit expressions for these generators
Showed they satisfy deformed commutation relations
Abstract
Using the second Drinfeld formulation of the quantized universal enveloping algebra we introduce a family of its Heisenberg-type elements which are endowed with a deformed commutator and satisfy properties similar to generators of a Heisenberg subalgebra. Explicit expressions for new family of generators are found.
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