Characteristic cycles for the loop Grassmannian and nilpotent orbits
Characteristic cycles for the loop Grassmannian and nilpotent orbits
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DOI：
10.1215/s0012-7094-99-09705-3
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发表时间：
1999-03
影响因子：
2.5
通讯作者：
S. Evens;I. Mirkovic
中科院分区：
文献类型：
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作者：
S. Evens;I. Mirkovic
α（X）是余正规丛到X的子流形的闭包的线性组合。直觉上，微局域多重性cα（）是α处的奇异性。在与表示论相关的设置中，群G作用于X，是G-等变的，并且微局部多重性在表示论中发挥着重要但仅部分理解的作用（参见（Ro）、（SV）、（ABV）和（KaSa），例如）。在本文中，我们计算微局部多重性的某些情况下感兴趣的表示论。设G是具有环群LG的连通约化群，P是LG的由具有正傅立叶系数的环构成的子群.则Grassmannian环LG/P =上的P -轨道λ对应于对偶可约群G的不可约表示L（λ）。对于环面的主权μ和λ，
α (X), which is a linear combination of closures of conormal bundles to submanifolds of X. Intuitively, the microlocal multiplicities cα() me asurethesingularity of at α. In settings related to representation theory, a group G acts on X, is G-equivariant, and the microlocal multiplicities play a significant but only partially understood role in representation theory (see (Ro), (SV), (ABV), and (KaSa), e.g.). In this paper, we compute microlocal multiplicities for certain cases of interest in representation theory. Let G be a connected reductive group with loop group LG, and let P bethesubgroup of LG consisting of loops with positive Fourier coefficients. Then P -orbits λ on theloop Grassmannian LG/P = correspond to the irreducible representations L(λ) of thedual re ductivegroup ˇ G. For dominant weights µ and λ of a torus of ˇ