Subset Representations and Eigenvalues of the Universal Intertwining Matrix
Dirk Siersma, Wilberd van der Kallen
TL;DR
This paper investigates the eigenvalues of the universal intertwining matrix related to subset representations and applies the findings to validate the ELK signature formula for degenerate stars.
Contribution
It provides a combinatorial analysis of eigenvalues of the universal intertwining endomorphism and applies it to a geometric signature formula validation.
Findings
Eigenvalues characterized combinatorially
Validation of the ELK signature formula for specific singularities
Enhanced understanding of subset representation eigenstructure
Abstract
We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation. This is then applied to justify the evaluation of the Eisenbud-Levine-Khimshiashvili (ELK) signature formula for the gradient index at a degenerate star in arXiv:2001.10882
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