A Categorification of the Spin Representation ofU(𝔰𝔬(7, ℂ)) via Projective Functors

DOI10.1080/00927872.2012.673041zbMath1278.17005arXiv1102.3952OpenAlexW2006663702MaRDI QIDQ2850833

Yongjun Xu, Shilin Yang

Publication date: 30 September 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.3952

zbMATH Keywords

spin representationcategorificationprojective functorBGG category \(\mathcal{O}\)

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10)

Cites Work

• Lectures on algebraic categorification
• Categorification of Wedderburn's basis for \({\mathbb{C}}[S_{n}\)]
• Categorification of (induced) cell modules and the rough structure of generalised Verma modules
• Category of \(\mathfrak g\) modules
• Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
• A categorification of the Temperley-Lieb algebra and Schur quotients of \(U(\mathfrak{sl}_2)\) via projective and Zuckerman functors
• Cell 2-representations of finitary 2-categories
• Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases
• Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module
• Clock and category: Is quantum gravity algebraic?
• A categorification of integral Specht modules
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