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The elliptic Weyl character formula
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 7 / July 2014
- Published online by Cambridge University Press:
- 12 May 2014, pp. 1196-1234
- Print publication:
- July 2014
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- Article
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We calculate equivariant elliptic cohomology of the partial flag variety
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where 
$H\subseteq G$ are compact connected Lie groups of equal rank. We identify the 
${\rm RO}(G)$-graded coefficients 
${\mathcal{E}} ll_G^*$ as powers of Looijenga’s line bundle and prove that transfer along the map is calculated by the Weyl–Kac character formula. Treating ordinary cohomology,
$$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$
$K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram, Elliptic Schubert calculus, in preparation].
