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arXiv · 2401.11473

Deformations of complete Pick spaces

Prahllad Deb·Jonathan Nureliyan·Eli Shamovich
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Abstract

Motivated by the work of Pandey, Ofek, and Shalit on the one hand and deformation theory on the other, we study the Grassmannian of $n$-dimensional multiplier-coinvariant subspaces of the Drury-Arveson space. We show that this space admits a natural map to the symmetrized polyball that induces an isomorphism between the configuration space of $n$ points in the ball and the subspace of projection onto spaces spanned by $n$ distinct kernels. We discuss the tautological bundle on our Grassmannian and the corresponding operator algebra bundle. We construct examples of bundles of complete Pick spaces from homogeneous hypersurfaces in $\mathbb{B}_d$. Along with these bundles, we construct examples of Cowen-Doulas tuples of operators from the compressed Arveson $d$-shift.

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Prahllad Deb, Jonathan Nureliyan, Eli Shamovich. 2024-01-21. Deformations of complete Pick spaces. https://arxiv.org/abs/2401.11473

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