Burge multipartitions and the AGT correspondence

Abstract

Abstract Burge multipartitions are tuples of partitions that satisfy a cyclic embedding condition. When uncoloured, Burge m-multipartitions give a combinatorial model for characters of the Wm algebras (W 2 is the Virasoro algebra). When n-coloured, they generalise the “cylindric partitions” that provide a combinatorial model (and a crystal graph) for integrable characters of the affine Lie algebra s l ^ ( n ) . Here, we show that the n-coloured Burge m-multipartitions yield the characters of the CFT cosets g l ^ ( d ) m / g l ^ ( d − n ) m . Having previously shown that the same combinatorial objects give the SU(m) instanton partition functions in 𝒩 = 2 supersymmetric gauge theories on ℂ2/ℤ n , we have thus established a wide-ranging extension of the AGT correspondence. This talk is based on a collaboration with N.Macleod (Melbourne).