تقرير
Characteristic equation for symplectic groupoid and cluster algebras
| العنوان: | Characteristic equation for symplectic groupoid and cluster algebras |
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| المؤلفون: | Chekhov, Leonid O., Shapiro, Michael, Shibo, Huang |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematical Physics, Mathematics - Quantum Algebra, 51H25 |
| الوصف: | We use the Darboux coordinate representation found by two of the authors (L.Ch. and M.Sh.) for entries of general symplectic leaves of the $\mathcal A_n$-groupoid of upper-triangular matrices to express roots of the characteristic equation $\det(\mathbb A-\lambda \mathbb A^{\text{T}})=0$, with $\mathbb A\in \mathcal A_n$, in terms of Casimirs of this Darboux coordinate representation, which is based on cluster variables of Fock--Goncharov higher Teichm\"uller spaces for the algebra $sl_n$. We show that roots of the characteristic equation are simple monomials of cluster Casimir elements. This statement remains valid in the quantum case as well. We consider a generalization of $\mathcal A_n$-groupoid to a $\mathcal A_{Sp_{2m}}$-groupoid. Comment: 15 pages, 7 figures, section on $Sp_{2m}$ groupoid added. arXiv admin note: text overlap with arXiv:2003.07499 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2101.10323 |
| رقم الأكسشن: | edsarx.2101.10323 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |