Higher level $q$-oscillator representations for $U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$ and $U_q(B^{(1)}(0,n))$

TL;DR

This paper constructs higher level q-oscillator representations for certain quantum affine (super)algebras, proving their irreducibility and explicitly computing their characters for specific types, advancing the understanding of these algebraic structures.

Contribution

It introduces a new class of higher level q-oscillator representations for types C and B quantum affine algebras, extending previous level one constructions via fusion.

Findings

Higher level q-oscillator representations are irreducible.

Explicit character formulas in terms of Schur polynomials for types C and C^{(2)}.

Construction via fusion procedure from level one representations.

Abstract

We introduce higher level $q$-oscillator representations for the quantum affine (super)algebras of type $C_n^{(1)},C^{(2)}(n+1)$ and $B^{(1)}(0,n)$. These representations are constructed by applying the fusion procedure to the level one $q$-oscillator representations which were obtained through the studies of the tetrahedron equation. We prove that these higher level $q$-oscillator representations are irreducible. For type $C_n^{(1)}$ and $C^{(2)}(n+1)$, we compute their characters explicitly in terms of Schur polynomials.