Higher Level q-Oscillator Representations for $$U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$$ and $$U_q(B^{(1)}(0,n))$$
| Autor: | Jae-Hoon Kwon, Masato Okado |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
010102 general mathematics Fusion procedure Statistical and Nonlinear Physics Type (model theory) 01 natural sciences Schur polynomial Combinatorics 17B37 17B67 Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Tetrahedron Quantum Algebra (math.QA) 010307 mathematical physics Affine transformation 0101 mathematics Quantum Mathematical Physics |
| Zdroj: | Communications in Mathematical Physics. 385:1041-1082 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-021-04009-x |
| Popis: | 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. 41 pages; Theorem 4.1 has been added, where we prove the irreducibility of the higher level $q$-oscillator representation in a uniform way. The proof is given in Appendix D |
| Databáze: | OpenAIRE |
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