Representation theory in complex rank. I.

DOI10.1007/s00031-014-9260-2zbMath1336.20011arXiv1401.6321OpenAlexW3043330606MaRDI QIDQ2249224

Pavel I. Etingof

Publication date: 10 July 2014

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6321

zbMATH Keywords

wreath productsrepresentations of symmetric groupstensor categoriesaffine Hecke algebrassymplectic reflection algebrasrepresentation categoriesrational Cherednik algebras

Mathematics Subject Classification ID

Related Items (15)

Representation theory in complex rank. II ⋮ Categories parametrized by schemes and representation theory in complex rank ⋮ Generators for the representation rings of certain wreath products ⋮ The indecomposable objects in the center of Deligne's category Re̲pSt$\protect\underline{{\rm Re}}\!\operatorname{p}S_t$ ⋮ New realizations of deformed double current algebras and Deligne categories ⋮ Sums of binomial coefficients evaluated at \(\alpha\in\overline{\mathbb{Q}}\), and applications ⋮ Modified traces on Deligne's category \(\underline{\mathrm{Re}}\mathrm p(S_t)\) ⋮ Classification of simple algebras in the Deligne category \(\operatorname{Rep}(S_t)\) ⋮ Embedding Deligne's category \(\underline{\mathrm{Re}}\mathrm{p}(S_t)\) in the Heisenberg category (with an appendix written with Christopher Ryba) ⋮ Stable Grothendieck rings of wreath product categories ⋮ Group partition categories ⋮ Deligne categories in lattice models and quantum field theory, \textit{or} making sense of O(N) symmetry with non-integer N ⋮ Dimensional interpolation and the Selberg integral ⋮ On representations of rational Cherednik algebras of complex rank ⋮ The spin-Brauer diagram algebra

Cites Work

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• Categories parametrized by schemes and representation theory in complex rank
• On representation categories of wreath products in non-integral rank
• On blocks of Deligne's category \(\underline {\text{Re}}\text p (S_t)\).
• Continuous Hecke algebras.
• Hodge cycles, motives, and Shimura varieties
• Classification of graded Hecke algebras for complex reflection groups.
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Tensor envelopes of regular categories
• A construction of semisimple tensor categories
• Schur–Weyl Duality for Deligne Categories
• On representations of rational Cherednik algebras of complex rank
• Intersecting families of permutations

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