c=3/2时的Super-Whittaker向量
Super-Whittaker vector at c=3/2
摘要：
超共形代数的退化Whittaker向量可以用Jack超多项式表示。然而，在这种表示中，惠特克向量的范数涉及杰克超多项式与之不正交的标量积。在本文中，我们指出，这个缺陷可以治愈在c=3/2的超对称情况下，通过特定的技巧。当c=3/2时，我们得到了退化超惠特克向量的范数的封闭表达式。假设AGT猜想的超级版本，这个封闭形式的表达式应该等于Z_2-对称SU（2）纯规范瞬子配分函数--相应的等式采取相当非平凡的组合恒等式的形式。
英文摘要：
The degenerate Whittaker vector of the superconformal algebra can be represented in terms of Jack superpolynomials. However, in this representation the norm of the Whittaker vector involves a scalar product with respect to which the Jack superpolynomials are not orthogonal. In this note, we point out that this defect can be cured at c=3/2 by means of a trick specific to the supersymmetric case. At c=3/2, we thus end up with a closed-form expression for the norm of the degenerate super-Whittaker vector. Granting the super-version of the AGT conjecture, this closed-form expression should be equal to the Z_2-symmetric SU(2) pure-gauge instanton partition function -- the corresponding equality taking the form of a rather nontrivial combinatorial identity.
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