论文标题
Sklyanin决定因素的次要身份
Minor identities for Sklyanin determinants
论文作者
论文摘要
我们通过采用R-Matrix技术来探索正交和符号类型的量子对称空间的不变理论。我们的重点涉及建立与正交和符号案例相关的量子决定因素，Sklyanin决定因素，以及在符号量子空间上的量子PFAFFIAN。我们从扭曲的扬吉人中汲取灵感，我们不仅展示了Q-Jacobi身份，Q-Cayley的互补身份，Q-Sylvester的身份以及Muir的适用性，以及在正交和符号类型中的Sklyanin Muir的适用性，以及在Q-Pfaffian类型中，以及在符合性场景中。此外，我们在准延迟剂方面介绍了Sklyanin决定因素和量子PFAFFIAN的表达式。
We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated with the orthogonal and symplectic cases, and the quantum Pfaffians over the symplectic quantum space. Drawing inspiration from twisted Yangians, we not only demonstrate but also extend the applicability of q-Jacobi identities, q-Cayley's complementary identities, q-Sylvester identities, and Muir's theorem to Sklyanin minors in both orthogonal and symplectic types, along with q-Pfaffian analogs in the symplectic scenario. Furthermore, we present expressions for Sklyanin determinants and quantum Pfaffians in terms of quasideterminants.
