Abstract
We characterize the irreducible representations of the general linear group GL(V) that have multiplicity 1 in the direct sum of all Schur modules of a given exterior power of V. These have come up in connection with the relations of the lower order minors of a generic matrix. We show that the minimal relations conjectured by Bruns, Conca and Varbaro are exactly those coming from partitions of single exterior type.
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*The authors thank the Mathematical Sciences Research Institute, Berkeley CA, where this work started to take shape, for support and hospitality during Fall 2012.
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BRUNS, W., VARBARO, M. PARTITIONS OF SINGLE EXTERIOR TYPE. Transformation Groups 19, 969–978 (2014). https://doi.org/10.1007/s00031-014-9280-y
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DOI: https://doi.org/10.1007/s00031-014-9280-y