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On blocks of Deligne’s category \(\underline {\text{Re}}\text p (S_t)\). (English) Zbl 1225.18005

Summary: We describe blocks in Deligne’s category \(\underline {\text{Re}}\text p (S_t)\) [see P. Deligne, Stud. Math., Tata Institute of Fundamental Research 19, 209–273 (2007; Zbl 1165.20300)].

MSC:

18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
20C30 Representations of finite symmetric groups

Citations:

Zbl 1165.20300

References:

[1] Bakalov, Bojko; Kirillov, Alexander, Lectures on Tensor Categories and Modular Functors, Univ. Lecture Ser., vol. 21 (2001), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI · Zbl 0965.18002
[2] Benson, D. J., Representations and cohomology. I, (Basic Representation Theory of Finite Groups and Associative Algebras. Basic Representation Theory of Finite Groups and Associative Algebras, Cambridge Stud. Adv. Math., vol. 30 (1991), Cambridge University Press: Cambridge University Press Cambridge) · Zbl 0718.20001
[3] Deligne, P., La catégorie des représentations du groupe symétrique \(S_t\), lorsque \(t\) n’est pas un entier naturel, (Algebraic Groups and Homogeneous Spaces. Algebraic Groups and Homogeneous Spaces, Tata Inst. Fund. Res. Stud. Math. (2007), Tata Inst. Fund. Res.: Tata Inst. Fund. Res. Mumbai), 209-273 · Zbl 1165.20300
[4] Doran, William F.; Wales, David B., The partition algebra revisited, J. Algebra, 231, 1, 265-330 (2000) · Zbl 0974.20013
[5] Frobenius, Ferdinand Georg, Über die charaktere der symmetrischen gruppe, (Gesammelte Abhandlungen. Bände III (1968), Springer-Verlag), 148-166 (1900), S’ber Akad. Wiss. Berlin, pp. 303-315;
[6] Fulton, William; Harris, Joe, Representation Theory, Grad. Texts in Math., vol. 129 (1991), Springer-Verlag: Springer-Verlag New York, a first course, Readings in Mathematics · Zbl 0744.22001
[7] Halverson, Tom; Ram, Arun, Partition algebras, European J. Combin., 26, 6, 869-921 (2005) · Zbl 1112.20010
[8] Knop, Friedrich, Tensor envelopes of regular categories, Adv. Math., 214, 2, 571-617 (2007) · Zbl 1127.18004
[9] Littlewood, D. E., Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Canad. J. Math., 10, 17-32 (1958) · Zbl 0079.03604
[10] Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Math. Monogr. (1995), The Clarendon Press Oxford University Press: The Clarendon Press Oxford University Press New York, with contributions by A. Zelevinsky, Oxford Science Publications · Zbl 0487.20007
[11] Martin, Paul, Potts Models and Related Problems in Statistical Mechanics, Ser. Adv. Statist. Mech., vol. 5 (1991), World Scientific Publishing Co., Inc.: World Scientific Publishing Co., Inc. Teaneck, NJ · Zbl 0734.17012
[12] Martin, Paul, Temperley-Lieb algebras for nonplanar statistical mechanics—the partition algebra construction, J. Knot Theory Ramifications, 3, 1, 51-82 (1994) · Zbl 0804.16002
[13] Martin, Paul, The structure of the partition algebras, J. Algebra, 183, 2, 319-358 (1996) · Zbl 0863.20009
[14] Westbury, B. W., The representation theory of the Temperley-Lieb algebras, Math. Z., 219, 4, 539-565 (1995) · Zbl 0840.16008
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