Abstract
A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. We prove that, in a general fractional-brane background, the identity persists in taking, for each character, the matrix integration of the super Chern-Simons matrix model in the grand canonical ensemble.
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