The Bloch-Okounkov correlation functions, a classical half-integral case

Details The Bloch-Okounkov correlation functions, a classical half-integral case The Bloch-Okounkov correlation functions, a classical half-integral case

2008-06-19

arxiv.org/abs/0806.3257v2

Mathematics

Representation Theory

v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physics

Scientific paper

10.1007/s11005-008-0263-6

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of $\hgl_\infty$-modules of level one. Recent works have calculated these character functions for higher levels for $\hgl_\infty$ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.

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