The quantum MacMahon Master Theorem

A New Proof of the Garoufalidis-Le-Zeilberger Quantum MacMahon Master Theorem

We propose a new proof of the quantum version of MacMahon's Master Theorem, established by Garoufalidis, Le and Zeilberger.

Specializations and Extensions of the quantum MacMahon Master Theorem

We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Le and Zeilberger. In particular, we obtain a (t,q)-analogue for the Cartier-Foata noncommutative version and a semi-strong (t,q)-analogue for the contextual algebra.

Koszul algebras and the quantum MacMahon Master Theorem

We give a new proof of the quantum version of MacMahon's Master Theorem due to Garoufalidis, Le and Zeilberger (one-parameter case) and to Konvalinka and Pak (multiparameter case) by deriving it from known facts about Koszul algebras.

The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for $\widehat{\mathfrak{gl}}(m|n)$

We prove an analogue of the MacMahon Master Theorem for the right quantum superalgebras. In particular, we obtain a new and simple proof of this theorem for the right quantum algebras. In the super case the theorem is then used to construct higher order Sugawara operators for the affine Lie superalgebra $\widehat{\mathfrak{gl}}(m|n)$ in an explicit form. The operators are elements of a completed universal enveloping algebra of $\widehat{\mathfrak{gl}}(m|n)$ at the critical level. They occur as the coefficients in the expansion of a noncommutative Berezinian and as the traces of powers of gener…

量子超Manin矩阵

Quantum super Manin matrices

本文针对超Manin矩阵的q-模拟展开研究，推导得到多个经典恒等式的量子对应形式，为量子空间线性变换相关的代数研究提供了新的恒等式工具。

量子仿射超代数 $U_q(\widehat{gl}_{M|N})$ 的量子 Berezinian

Quantum Berezinian for quantum affine superalgebra $U_q(\widehat{gl}_{M|N})$

本文引入量子仿射超代数的量子 Berezinian，证明其系数属于中心，构造另一族中心元素，并证明多个矩阵定理的类似物。