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Virasoro irregular conformal block is presented as the expectation value ofJack-polynomials of the beta-deformed Penner-type matrix model and is comparedwith the inner product of Gaiotto states with arbitrary rank. It is confirmedthat there are non-trivial modifications of the Gaiotto states due to thenormalization of the states. The relation between the two is explicitly checkedfor rank 2 irregular conformal block.

Virasoro irregular conformal block and beta deformed random matrix model