메뉴 건너뛰기




Volumn 8, Issue 4, 2003, Pages 321-332

Lower bounds for Kazhdan-Lusztig polynomials from patterns

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0141904901     PISSN: 10834362     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00031-003-0629-x     Document Type: Article
Times cited : (36)

References (33)
  • 2
    • 0030528385 scopus 로고    scopus 로고
    • Koszul duality patterns in representation theory
    • [BGS]
    • [BGS] A. Beilinson, V. Ginzburg, W. Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), No. 2, 473-527.
    • (1996) J. Amer. Math. Soc. , vol.9 , Issue.2 , pp. 473-527
    • Beilinson, A.1    Ginzburg, V.2    Soergel, W.3
  • 3
    • 0009409406 scopus 로고    scopus 로고
    • Pattern avoidance and rational smoothness of Schubert varieties
    • [Bi]
    • [Bi] S. Billey, Pattern avoidance and rational smoothness of Schubert varieties, Adv. Math. 139 (1998), No. 1, 141-156.
    • (1998) Adv. Math. , vol.139 , Issue.1 , pp. 141-156
    • Billey, S.1
  • 4
    • 0033114760 scopus 로고    scopus 로고
    • The parabolic map
    • [BiFL]
    • [BiFL] S. Billey, C. K. Fan, J. Losonczy, The parabolic map, J. Algebra, 214 (1999), No. 1, 1-7.
    • (1999) J. Algebra , vol.214 , Issue.1 , pp. 1-7
    • Billey, S.1    Fan, C.K.2    Losonczy, J.3
  • 6
    • 0035274906 scopus 로고    scopus 로고
    • Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
    • [BiW1]
    • [BiW1] S. Billey, G. Warrington, Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations, J. Alg. Comb. 13 (2000), 111-136.
    • (2000) J. Alg. Comb. , vol.13 , pp. 111-136
    • Billey, S.1    Warrington, G.2
  • 7
    • 0242382109 scopus 로고    scopus 로고
    • Maximal singular loci of Schubert varieties in SL(n)/B
    • [BiW2]
    • [BiW2] S. Billey, G. Warrington, Maximal singular loci of Schubert varieties in SL(n)/B, Trans. Amer. Math. Soc. 355 (2003), No. 10, 3915-3945.
    • (2003) Trans. Amer. Math. Soc. , vol.355 , Issue.10 , pp. 3915-3945
    • Billey, S.1    Warrington, G.2
  • 8
    • 0141888392 scopus 로고    scopus 로고
    • Hyperbolic localization of intersection cohomology
    • [Br]
    • [Br] T. Braden, Hyperbolic localization of intersection cohomology, Transformation Groups 8 (2003), No. 3, 209-216.
    • (2003) Transformation Groups , vol.8 , Issue.3 , pp. 209-216
    • Braden, T.1
  • 9
    • 0005556651 scopus 로고    scopus 로고
    • Intersection homology of toric varieties and a conjecture of Kalai
    • [BrM]
    • [BrM] T. Braden, R. MacPherson, Intersection homology of toric varieties and a conjecture of Kalai, Comment. Math. Helv. 74 (1999), No. 3, 442-455.
    • (1999) Comment. Math. Helv. , vol.74 , Issue.3 , pp. 442-455
    • Braden, T.1    Macpherson, R.2
  • 10
    • 0035646682 scopus 로고    scopus 로고
    • From moment graphs to intersection cohomology
    • [BrM2]
    • [BrM2] T. Braden, R. MacPherson, From moment graphs to intersection cohomology, Math. Ann. 321 (2001) No. 3, 533-551.
    • (2001) Math. Ann. , vol.321 , Issue.3 , pp. 533-551
    • Braden, T.1    Macpherson, R.2
  • 11
    • 0242270291 scopus 로고    scopus 로고
    • Explicit formulae for some Kazhdan-Lusztig polynomials
    • [BreS]
    • [BreS] F. Brenti, R. Simion, Explicit formulae for some Kazhdan-Lusztig polynomials, J. Alg. Comb. 11 (2000), No. 3, 187-196.
    • (2000) J. Alg. Comb. , vol.11 , Issue.3 , pp. 187-196
    • Brenti, F.1    Simion, R.2
  • 12
    • 0001028633 scopus 로고
    • Kazhdan-Lusztig conjecture and holonomic systems
    • [BryK]
    • [BryK] J.-L. Brylinski, M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), No. 3, 387-410.
    • (1981) Invent. Math. , vol.64 , Issue.3 , pp. 387-410
    • Brylinski, J.-L.1    Kashiwara, M.2
  • 13
    • 0001844911 scopus 로고
    • The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties
    • [C]
    • [C] J. Carrell, The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties, Proc. Symp. Pure Math., AMS 56 (1994), 53-61.
    • (1994) Proc. Symp. Pure Math., AMS , vol.56 , pp. 53-61
    • Carrell, J.1
  • 14
    • 0037933482 scopus 로고    scopus 로고
    • Smooth points of T-stable varieties in G/B and the Peterson map
    • [CK]
    • [CK] J. Carrell, J. Kuttler, Smooth points of T-stable varieties in G/B and the Peterson map, Invent. Math. 151 (2003), 353-379.
    • (2003) Invent. Math. , vol.151 , pp. 353-379
    • Carrell, J.1    Kuttler, J.2
  • 15
    • 0040438501 scopus 로고    scopus 로고
    • Singularités génériques des variétés de Schubert covexillaires
    • [Co]
    • [Co] A. Cortez, Singularités génériques des variétés de Schubert covexillaires, Ann. Inst. Fourier (Grenoble) 51 (2001), No. 2, 375-393.
    • (2001) Ann. Inst. Fourier (Grenoble) , vol.51 , Issue.2 , pp. 375-393
    • Cortez, A.1
  • 16
    • 0043240893 scopus 로고    scopus 로고
    • Singularités génériques et quasi-resolutions des variétés de Schubert pour le groupe linéaire
    • [Co2]
    • [Co2] A. Cortez, Singularités génériques et quasi-resolutions des variétés de Schubert pour le groupe linéaire, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), No. 6, 561-566.
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , Issue.6 , pp. 561-566
    • Cortez, A.1
  • 17
    • 0013137719 scopus 로고
    • Local Poincaré duality and nonsingularity of Schubert varieties
    • [De]
    • [De] V. Deodhar, Local Poincaré duality and nonsingularity of Schubert varieties, Comm. Algebra 13 (1985), No. 6, 1379-1388.
    • (1985) Comm. Algebra , vol.13 , Issue.6 , pp. 1379-1388
    • Deodhar, V.1
  • 19
    • 0347486421 scopus 로고
    • A fixed-point characterization of linearly reductive groups
    • [FN] (collection of papers dedicated to Ellis Kolchin), Academic Press, New York
    • [FN] J. Fogarty, P. Norman, A fixed-point characterization of linearly reductive groups, in: Contributions to Algebra (collection of papers dedicated to Ellis Kolchin), Academic Press, New York, 1977, pp. 151-155.
    • (1977) Contributions to Algebra , pp. 151-155
    • Fogarty, J.1    Norman, P.2
  • 20
  • 21
    • 0002340487 scopus 로고
    • The socle filtration of a Verma module
    • [I]
    • [I] R. Irving, The socle filtration of a Verma module, Ann. Sci. École Norm. Sup. (series 4) 21 (1988), No. 1, 47-65.
    • (1988) Ann. Sci. École Norm. Sup. (Series 4) , vol.21 , Issue.1 , pp. 47-65
    • Irving, R.1
  • 22
    • 34250264460 scopus 로고
    • Representations of Coxeter groups and Hecke algebras
    • [KL1]
    • [KL1] D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math., 53 (1979), 165-184.
    • (1979) Invent. Math. , vol.53 , pp. 165-184
    • Kazhdan, D.1    Lusztig, G.2
  • 23
    • 0003206873 scopus 로고
    • Schubert varieties and Poincaré duality
    • [KL2]
    • [KL2] D. Kazhdan, G. Lusztig, Schubert varieties and Poincaré duality, Proc. Symp. Pure. Math., AMS 36 (1980), 185-203.
    • (1980) Proc. Symp. Pure. Math., AMS , vol.36 , pp. 185-203
    • Kazhdan, D.1    Lusztig, G.2
  • 24
    • 84968484974 scopus 로고
    • Intersection homology and torus actions
    • [Ki]
    • [Ki] F. Kirwan, Intersection homology and torus actions, J. Amer. Math. Soc. 1 (1988), No. 2, 385-400.
    • (1988) J. Amer. Math. Soc. , vol.1 , Issue.2 , pp. 385-400
    • Kirwan, F.1
  • 25
    • 0002099330 scopus 로고
    • Criterion for smoothness of Schubert varieties in Sl(n)/B
    • [LS]
    • [LS] V. Lakshmibai, B. Sandhya, Criterion for smoothness of Schubert varieties in Sl(n)/B Proc. Indian Acad. Sci. Math. Sci. 100 (1990), No. 1, 45-52.
    • (1990) Proc. Indian Acad. Sci. Math. Sci. , vol.100 , Issue.1 , pp. 45-52
    • Lakshmibai, V.1    Sandhya, B.2
  • 26
    • 0001482950 scopus 로고
    • Polynômes de Kazhdan and Lusztig pour les grassmanniennes
    • [LasSc] Young Tableaux and Schur Functions in Algebra and Geometry Toruń
    • [LasSc] A. Lascoux, M. P. Schützenberger, Polynômes de Kazhdan and Lusztig pour les grassmanniennes, in: Young Tableaux and Schur Functions in Algebra and Geometry (Toruń, 1980), Astérisque 87-88 (1981), 249-266.
    • (1980) Astérisque , vol.87-88 , pp. 249-266
    • Lascoux, A.1    Schützenberger, M.P.2
  • 27
    • 0242270292 scopus 로고    scopus 로고
    • The singular locus of a Schubert variety
    • [KLR] Prépublication de l'Institut de Recherche Mathématique Avancée
    • [KLR] C. Kassel, A. Lascoux and C. Reutenauer, The singular locus of a Schubert variety, Prépublication de l'Institut de Recherche Mathématique Avancée (2001). To appear J. of Algebra.
    • (2001) J. of Algebra
    • Kassel, C.1    Lascoux, A.2    Reutenauer, C.3
  • 28
    • 0346251627 scopus 로고    scopus 로고
    • Le lieu singulier des variétés de Schubert
    • [Ma]
    • [Ma] L. Manivel, Le lieu singulier des variétés de Schubert, Internat. Math. Res. Notices (2001), No. 16, 849-871.
    • (2001) Internat. Math. Res. Notices , Issue.16 , pp. 849-871
    • Manivel, L.1
  • 29
    • 85009830023 scopus 로고    scopus 로고
    • Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups
    • [P] (electronic)
    • [P] P. Polo, Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups, Represent. Theory 3 (1999), 90-104 (electronic).
    • (1999) Represent. Theory , vol.3 , pp. 90-104
    • Polo, P.1
  • 30
    • 0012522479 scopus 로고
    • On Schubert varieties in the flag manifold of Sl(n,C)
    • [R]
    • [R] K. M. Ryan, On Schubert varieties in the flag manifold of Sl(n,C), Math. Ann. 276 (1987), No. 2, 205-224.
    • (1987) Math. Ann. , vol.276 , Issue.2 , pp. 205-224
    • Ryan, K.M.1
  • 31
    • 0003208801 scopus 로고    scopus 로고
    • Linear Algebraic Groups, Second edition
    • [Sp] Birkhäuser, Boston, MA
    • [Sp] T. Springer, Linear Algebraic Groups, Second edition, Progr. in Math.' Vol. 9, Birkhäuser, Boston, MA, 1998.
    • (1998) Progr. in Math. , vol.9
    • Springer, T.1
  • 32
    • 0000906088 scopus 로고    scopus 로고
    • On the fully commutative elements of Coxeter groups
    • [St]
    • [St] J. Stembridge, On the fully commutative elements of Coxeter groups, J. Alg. Comb. 5 (1996), No. 4, 353-385.
    • (1996) J. Alg. Comb. , vol.5 , Issue.4 , pp. 353-385
    • Stembridge, J.1
  • 33
    • 38249024475 scopus 로고
    • A combinatorial approach to the singularities of Schubert varieties
    • [W]
    • [W] J. S. Wolper, A combinatorial approach to the singularities of Schubert varieties, Adv. Math. 76 (1989), No. 2, 184-193.
    • (1989) Adv. Math. , vol.76 , Issue.2 , pp. 184-193
    • Wolper, J.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.