Orthosymplectic $R$-matrices
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913131121344512 |
|---|---|
| author | Hong, Kyungtak Tsymbaliuk, Alexander |
| author_facet | Hong, Kyungtak Tsymbaliuk, Alexander |
| contents | We present a formula for trigonometric orthosymplectic $R$-matrices associated with any parity sequence, and establish their factorization into the ordered product of $q$-exponents parametrized by positive roots in the corresponding reduced root systems. The latter is crucially based on the construction of orthogonal bases of the positive subalgebra through $q$-bracketings and combinatorics of dominant Lyndon words, as developed in [Clark, Hill, Wang, "Quantum shuffles and quantum supergroups of basic type", Quantum Topol. 7 (2016), no.3, 553-638]. We further evaluate the affine orthosymplectic $R$-matrices, establishing their intertwining property as well as matching them with those obtained through the Yang-Baxterization technique of [Ge, Wu, Xue, "Explicit trigonometric Yang-Baxterization", Internat. J. Modern Phys. A 6 (1991), no.21, 3735-3779]. This reproduces the celebrated formulas of [Jimbo, "Quantum $R$ matrix for the generalized Toda system", Comm. Math. Phys. 102 (1986), no.4, 537-547] for classical BCD types and the formula of [Mehta, Dancer, Gould, Links, "Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras", J. Phys. A 39 (2006), no.1, 17-26] for the standard parity sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthosymplectic $R$-matrices Hong, Kyungtak Tsymbaliuk, Alexander Representation Theory High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems We present a formula for trigonometric orthosymplectic $R$-matrices associated with any parity sequence, and establish their factorization into the ordered product of $q$-exponents parametrized by positive roots in the corresponding reduced root systems. The latter is crucially based on the construction of orthogonal bases of the positive subalgebra through $q$-bracketings and combinatorics of dominant Lyndon words, as developed in [Clark, Hill, Wang, "Quantum shuffles and quantum supergroups of basic type", Quantum Topol. 7 (2016), no.3, 553-638]. We further evaluate the affine orthosymplectic $R$-matrices, establishing their intertwining property as well as matching them with those obtained through the Yang-Baxterization technique of [Ge, Wu, Xue, "Explicit trigonometric Yang-Baxterization", Internat. J. Modern Phys. A 6 (1991), no.21, 3735-3779]. This reproduces the celebrated formulas of [Jimbo, "Quantum $R$ matrix for the generalized Toda system", Comm. Math. Phys. 102 (1986), no.4, 537-547] for classical BCD types and the formula of [Mehta, Dancer, Gould, Links, "Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras", J. Phys. A 39 (2006), no.1, 17-26] for the standard parity sequence. |
| title | Orthosymplectic $R$-matrices |
| topic | Representation Theory High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2408.16720 |