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November 2019 Hyperplane Arrangements and Tensor Product Invariants
P. Belkale, P. Brosnan, S. Mukhopadhyay
Michigan Math. J. 68(4): 801-829 (November 2019). DOI: 10.1307/mmj/1565251217

Abstract

In the first part of this paper, we consider, in the context of an arbitrary weighted hyperplane arrangement, the map from compactly supported cohomology to the usual cohomology of a local system. We obtain a formula (i.e., an explicit algebraic de Rham representative) for a generalized version of this map.

In the second part, we apply these results to invariant theory: Schechtman and Varchenko connect invariant theoretic objects to the cohomology of local systems on complements of hyperplane arrangements. The first part of this paper is then used, following and completing arguments of Looijenga, to determine the image of invariants in cohomology. In suitable cases (e.g., corresponding to positive integral levels) the space of invariants acquires a mixed Hodge structure over a cyclotomic field. We investigate the Hodge filtration on the space of invariants and characterize the subspace of conformal blocks in Hodge theoretic terms.

Citation

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P. Belkale. P. Brosnan. S. Mukhopadhyay. "Hyperplane Arrangements and Tensor Product Invariants." Michigan Math. J. 68 (4) 801 - 829, November 2019. https://doi.org/10.1307/mmj/1565251217

Information

Received: 17 November 2017; Revised: 7 December 2018; Published: November 2019
First available in Project Euclid: 8 August 2019

zbMATH: 07155050
MathSciNet: MR4029630
Digital Object Identifier: 10.1307/mmj/1565251217

Subjects:
Primary: 14D07, 32G34, 81T40

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 4 • November 2019
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