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Dedekind’s $$\eta$$-function and Rogers-Ramanujan identities. (English) Zbl 1234.05040
Summary: We prove a $$q$$-series identity that generalizes Macdonald’s $$A_{2n}^{(2)} \eta$$-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalize even further to also include the Andrews-Gordon identities.

##### MSC:
 05A19 Combinatorial identities, bijective combinatorics 05E05 Symmetric functions and generalizations 11F20 Dedekind eta function, Dedekind sums 33D67 Basic hypergeometric functions associated with root systems
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