"Birman–Murakami-Wenzl algebra"의 두 판 사이의 차이
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2020년 11월 13일 (금) 07:08 판
introduction
- Birman–Murakami-Wenzl algebra, a deformation of the Brauer algebra.
- has the Hecke algebra of type A as a quotient
- its specializations play a role in types B,C,D akin to that of the symmetric group in Schur-Weyl duality
history
- In 1984, Vaughan Jones introduced a new polynomial invariant of link isotopy types which is called the Jones polynomial.
- The invariants are related to the traces of irreducible representations of Hecke algebras associated with the symmetric groups.
- In 1986, Murakami (1986) showed that the Kauffman polynomial can also be interpreted as a function F on a certain associative algebra.
- In 1989, Birman & Wenzl (1989) constructed a two-parameter family of algebras $C_n(\ell, m)$ with the Kauffman polynomial $K_n(\ell, m)$ as trace after appropriate renormalization.
expositions
- Ariki, Susumu. 2006. “Algebras Arising from Schur-Weyl Type Dualities.” In Proceedings of the 38th Symposium on Ring Theory and Representation Theory, 1–10. Symp. Ring Theory Represent. Theory Organ. Comm., Yamanashi. http://www.ams.org/mathscinet-getitem?mr=2264119.
- Benkart, Georgia. 1996. “Commuting Actions—a Tale of Two Groups.” In Lie Algebras and Their Representations (Seoul, 1995), 194:1–46. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=1395593.
- Schüler, Axel. 1993. “The Brauer Algebra and the Birman-Wenzl-Murakami Algebra.” Seminar Sophus Lie 3 (1): 3–11. http://www.heldermann-verlag.de/jlt/jlt03/SCHUELAT.PDF
articles
- Rui, Hebing, and Linliang Song. “Mixed Schur-Weyl Duality between General Linear Lie Algebras and Cyclotomic Walled Brauer Algebras.” arXiv:1509.05855 [math], September 19, 2015. http://arxiv.org/abs/1509.05855.
- Rui, Hebing, and Linliang Song. ‘Decomposition Matrices of Birman-Murakami-Wenzl Algebras’. arXiv:1411.3067 [math], 11 November 2014. http://arxiv.org/abs/1411.3067.
- Li, Ge. “A KLR Grading of the Brauer Algebras.” arXiv:1409.1195 [math], September 3, 2014. http://arxiv.org/abs/1409.1195.
- Morton, H. R. “A Basis for the Birman-Wenzl Algebra.” arXiv:1012.3116 [math], December 14, 2010. http://arxiv.org/abs/1012.3116.