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引用次数: 0
摘要
q、t变形的Virasoro和\({mathcal {W}}\)-代数的共形块是表示理论中重要的特殊函数,在几何和物理中都有应用。在涅克拉索夫-沙塔什维利(Nekrasov-Shatashvili)极限(t \rightarrow 1\)中,只要其中一个表示是退化的,那么保角块就会满足与该退化表示相关的坐标的差分方程。这就是适当相对论量子可积分系统的静态薛定谔方程。预计泛化到一般的 \(t \ne 1\) 是一个非稳态薛定谔方程,其中 t 参数表示时间上的移动。在本文中,我们利用与麦克唐纳多项式的偶发关系,明确了具有一个退化模块和四个泛型维尔马模块的q,t-Virasoro块的非稳态方程,并证明了当五个模块中有三个模块退化时的非稳态方程。
Non-stationary difference equation for q-Virasoro conformal blocks
Conformal blocks of q, t-deformed Virasoro and \({\mathcal {W}}\)-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov–Shatashvili limit \(t \rightarrow 1\), whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic \(t \ne 1\) is a non-stationary Schrodinger equation where t parametrizes shift in time. In this paper we make the non-stationary equation explicit for the q, t-Virasoro block with one degenerate and four generic Verma modules and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.