Restricting Specht modules of cyclotomic Hecke algebras
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摘要
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
引文
1 Ariki S.On the semi-simplicity of the Hecke algebra of(Z/rZ)■_n.J Algebra,1994,169:216-225
2 Ariki S.Representations of Quantum Algebras and Combinatorics of Young Tableaux.Providence:Amer Math Soc,2002
3 Ariki S,Koike K.A Hecke algebra of(Z/rZ)■_n and construction of its irreducible representations.Adv Math,1994,106:216-243
4 Ariki S,Mathas A.The number of simple modules of the Hecke algebras of type G(r,1,n).Math Z,2000,233:601-623
5 Ariki S,Mathas A,Rui H.Cyclotomic Nazarov-Wenzl algebras.Nagoya Math J,2006,182:47-134
6 Broue M,Malle G.Zyklotomische Heckealgebren.Astérisque,1993,212:119-189
7 Brundan J.Centers of degenerate cyclotomic Hecke algebras and parabolic category O.Represent Theory,2008,12:236-259
8 Brundan J,Kleshchev A.Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras.Invent Math,2009,178:451-484
9 Brundan J,Kleshchev A.Graded decomposition numbers for cyclotomic Hecke algebras.Adv Math,2009,222:1883-1942
10 Brundan J,Kleshchev A,Wang W.Graded Specht modules.J Reine Angew Math,2011,655:61-87
11 Dipper R,James G,Mathas A.Cyclotomic q-Schur algebras.Math Z,1998,229:385-416
12 Goodman F M,Kilgore R,Teff N.A cell filtration of the restriction of a cell module.ArXiv:1504.02136,2015
13 Graham J J,Lehrer G I.Cellular algebras.Invent Math,1996,123:1-34
14 Hoefsmit P N.Representations of Hecke algebras of finite groups with BN-pairs of classical types.PhD Thesis.Vancouver:University of British Columbia,1974
15 Hu J,Mathas A.Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A.Adv Math,2010,225:598-642
16 Hu J,Mathas A.Graded induction for Specht modules.Int Math Res Not IMRN,2012,2012:1230-1263
17 Hu J,Mathas A.Seminormal forms and cyclotomic quiver Hecke algebras of type A.Math Ann,2016,364:1189-1254
18 James G,Mathas A.The Jantzen sum formula for cyclotomic q-Schur algebras.Trans Amer Math Soc,2000,352:5381-5404
19 Khovanov M,Lauda A D.A diagrammatic approach to categorification of quantum groups,I.Represent Theory,2009,13:309-347
20 Kleshchev A,Mathas A,Ram A.Universal graded Specht modules for cyclotomic Hecke algebras.Proc Lond Math Soc(3),2012,105:1245-1289
21 Li G.Integral basis theorem of cyclotomic khovanov-lauda-rouquier algebras of type A.J Algebra,2017,482:1-101
22 Lyle S,Mathas A.Blocks of cyclotomic Hecke algebras.Adv Math,2007,216:854-878
23 Mathas A.Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group.Providence:Amer Math Soc,1999
24 Mathas A.A Specht filtration of an induced Specht module.J Algebra,2009,322:893-902
25 Mathas A.Cyclotomic quiver Hecke algebras of type A.In:Teck G W,Tan K M,eds.Modular Representation Theory of Finite and p-Adic Groups.National University of Singapore Lecture Notes Series,vol.30.Singapore:World Scientific,2015,165-266
26 Rouquier R.2-Kac-Moody algebras.ArXiv:0812.5023,2008
27 Ryom-Hansen S.Grading the translation functors in type A.J Algebra,2004,274:138-163
28 Young A.On quantitative substitutional analysis I.Proc Lond Math Soc(3),1900,33:97-145
1)Professor Ariki disagrees that there is a gap in the original proof in[4].He says that the result can be easily deduced from[2,Theorem 13.21(2)]using the fact that the generator of the Specht module is a simultaneous eigenvector for the Jucys-Murphy elements.
2)Personal communication.See also[12].
2 Ariki S.Representations of Quantum Algebras and Combinatorics of Young Tableaux.Providence:Amer Math Soc,2002
3 Ariki S,Koike K.A Hecke algebra of(Z/rZ)■_n and construction of its irreducible representations.Adv Math,1994,106:216-243
4 Ariki S,Mathas A.The number of simple modules of the Hecke algebras of type G(r,1,n).Math Z,2000,233:601-623
5 Ariki S,Mathas A,Rui H.Cyclotomic Nazarov-Wenzl algebras.Nagoya Math J,2006,182:47-134
6 Broue M,Malle G.Zyklotomische Heckealgebren.Astérisque,1993,212:119-189
7 Brundan J.Centers of degenerate cyclotomic Hecke algebras and parabolic category O.Represent Theory,2008,12:236-259
8 Brundan J,Kleshchev A.Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras.Invent Math,2009,178:451-484
9 Brundan J,Kleshchev A.Graded decomposition numbers for cyclotomic Hecke algebras.Adv Math,2009,222:1883-1942
10 Brundan J,Kleshchev A,Wang W.Graded Specht modules.J Reine Angew Math,2011,655:61-87
11 Dipper R,James G,Mathas A.Cyclotomic q-Schur algebras.Math Z,1998,229:385-416
12 Goodman F M,Kilgore R,Teff N.A cell filtration of the restriction of a cell module.ArXiv:1504.02136,2015
13 Graham J J,Lehrer G I.Cellular algebras.Invent Math,1996,123:1-34
14 Hoefsmit P N.Representations of Hecke algebras of finite groups with BN-pairs of classical types.PhD Thesis.Vancouver:University of British Columbia,1974
15 Hu J,Mathas A.Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A.Adv Math,2010,225:598-642
16 Hu J,Mathas A.Graded induction for Specht modules.Int Math Res Not IMRN,2012,2012:1230-1263
17 Hu J,Mathas A.Seminormal forms and cyclotomic quiver Hecke algebras of type A.Math Ann,2016,364:1189-1254
18 James G,Mathas A.The Jantzen sum formula for cyclotomic q-Schur algebras.Trans Amer Math Soc,2000,352:5381-5404
19 Khovanov M,Lauda A D.A diagrammatic approach to categorification of quantum groups,I.Represent Theory,2009,13:309-347
20 Kleshchev A,Mathas A,Ram A.Universal graded Specht modules for cyclotomic Hecke algebras.Proc Lond Math Soc(3),2012,105:1245-1289
21 Li G.Integral basis theorem of cyclotomic khovanov-lauda-rouquier algebras of type A.J Algebra,2017,482:1-101
22 Lyle S,Mathas A.Blocks of cyclotomic Hecke algebras.Adv Math,2007,216:854-878
23 Mathas A.Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group.Providence:Amer Math Soc,1999
24 Mathas A.A Specht filtration of an induced Specht module.J Algebra,2009,322:893-902
25 Mathas A.Cyclotomic quiver Hecke algebras of type A.In:Teck G W,Tan K M,eds.Modular Representation Theory of Finite and p-Adic Groups.National University of Singapore Lecture Notes Series,vol.30.Singapore:World Scientific,2015,165-266
26 Rouquier R.2-Kac-Moody algebras.ArXiv:0812.5023,2008
27 Ryom-Hansen S.Grading the translation functors in type A.J Algebra,2004,274:138-163
28 Young A.On quantitative substitutional analysis I.Proc Lond Math Soc(3),1900,33:97-145
1)Professor Ariki disagrees that there is a gap in the original proof in[4].He says that the result can be easily deduced from[2,Theorem 13.21(2)]using the fact that the generator of the Specht module is a simultaneous eigenvector for the Jucys-Murphy elements.
2)Personal communication.See also[12].