Identities for Hypergeometric Integrals of Different Dimensions
Tóm tắt
Given complex numbers m1, I1 and nonnegative integers m2, I2, such that m1+m2 = I1+ I2, we define I2-dimensional hypergeometric integrals Ia,b(z; m1, m2, I1, I2), a,b = 0,. . . ,min)(m2,I2), depending on a complex parameter z. We show that Ia,b(z;m1, m2,I1, I2) = Ia,b(z;I1, I2,m1,m2), thus establishing an equality of I2 and m2-dimensional integrals. This identity allows us to study asymptotics of the integrals with respect to their dimension in some examples. The identity is based on the (
$$\cal{g l}$$
k,
$$\cal{g l}$$
k,) duality for the KZ and dynamical differential equations.
Tài liệu tham khảo
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