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We set up a framework for discussing `$q$-analogues of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras satisfying certain conditions introduced by Procesi and De Concini.
Let $mathscr{C}$ be the category of finite dimensional modules over the quantum affine algebra $U_q(widehat{mathfrak{g}})$ of a simple complex Lie algebra ${mathfrak{g}}$. Let $mathscr{C}^-$ be the subcategory introduced by Hernandez and Leclerc. We
We introduce a factorized difference operator L(u) annihilated by the Frenkel-Reshetikhin screening operator for the quantum affine algebra U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental q-characters, and establish a number
The concept of $lambda$-differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the $lambda$-differential Lie algebraic structure on the Witt algebra and the Virasoro algebra
In the framework of (vector valued) quantized holomorphic functions defined on non-commutative spaces, ``quantized hermitian symmetric spaces, we analyze what the algebras of quantized differential operators with variable coefficients should be. It i
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendiecks notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are replaced by D