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Quantum continuous $gl_\infty$: Tensor products of Fock modules and $W_n$ characters
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abstract
We construct a family of irreducible representations of the quantum continuous $gl_\infty$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $gl_n$ type. In particular, we obtain a simple combinatorial model for all representations of the $W_n$-algebras appearing in the minimal models in terms of $n$ interrelating partitions.
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Gauge Origami and BPS/CFT correspondence
The gauge origami partition function on C4 is realized as a correlation function of BPS qq-character operators, with D6 and D8 characters labeled by plane and solid partitions.
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