RSK bases and Kazhdan-Lusztig cells

Raghavan, K. N.; Samuel, Preena; Subrahmanyam, K. V.

Annales de l'Institut Fourier, Tome 62 (2012) no. 2, pp. 525-569.

À partir des caractérisations combinatoires des cellules de Kazhdan-Lusztig du groupe symétrique, on construit des bases “RSK” pour certains quotients du l’algèbre du groupe et de l’algèbre de Hecke. On étudie des applications à la théorie des invariants du groupe linéaire général sur divers anneaux de base et à la théorie des réprésentations, soit ordinaire ou modulaire, du groupe symétrique.

From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, “ RSK bases” are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetric group are discussed.

Classification : 05E10, 05E15, 20C08, 20C30
Keywords: Symmetric group, Hecke algebra, Kazhdan-Lusztig basis, RSK correspondence
Mot clés : groupe symétrique, algèbre de Hecke, base de Kazhdan-Lusztig, correspondance de RSK, forme de RSK, cellules de Kazhdan-Lusztig, invariants multilinéaire, invariants de desseins, module de cellule, module de Specht, déterminant de Gram, conjecture de Carter

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