@article{RSMUP_2000__104__201_0, author = {Vavilov, Nikolai}, title = {A third look at weight diagrams}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, volume = {104}, year = {2000}, pages = {201-250}, mrnumber = {1809357}, zbl = {1016.20029}, language = {en}, url = {http://dml.mathdoc.fr/item/RSMUP_2000__104__201_0} }
Vavilov, Nikolai. A third look at weight diagrams. Rendiconti del Seminario Matematico della Università di Padova, Tome 104 (2000) pp. 201-250. http://gdmltest.u-ga.fr/item/RSMUP_2000__104__201_0/
[A] Chevalley groups over local rings, Tôhoku Math. J., 21, no. 3 (1969), pp. 474-494. | MR 258837 | Zbl 0188.07201
,[A1] The 27-dimensional module for E6, I, Inv. Math., 89, no. 1 (1987), pp. 159-195. | MR 892190 | Zbl 0629.20018
,[A2] Some multilinear forms with large isometry groups, Geom. dedic., 25, no. 1-3 (1988), pp. 417-465. | MR 925846 | Zbl 0646.20033
,[A2] The geometry of trilinear forms, Finite Geometries, Buildings and Related topics, Oxford Univ. Press, 1990, pp. 75-84. | MR 1072156 | Zbl 0752.11020
,[ABS] On the structure of parabolic subgroups, Commun. Algebra, 18 (1990), pp. 551-562. | MR 1047327 | Zbl 0717.20029
- - ,[BV] Structure of hyperbolic unitary groups I, Elementary subgroup, Algebra Colloquim, 7, no. 2 (2000), pp. 159-196. | MR 1810843 | Zbl 0963.20024
- ,[BE] The Penrose transform, its interactions with representation theory, Clarendon Press, 1984. | MR 1038279 | Zbl 0726.58004
- ,[B] Properties and linear representations of Chevalley groups, Lecture Notes Math., 131 (1970), pp. 1-55. | MR 258838 | Zbl 0197.30501
,[B1] Groupes et algèbres de Lie. Ch. 4-6, Hermann, Paris, 1968. | MR 240238 | Zbl 0483.22001
,[B2] Groupes et algèbres de Lie. Ch. 7, 8, Hermann, Paris, 1975. | MR 453824
,[BCN] Distance regular graphs, Springer-Verlag, N. Y. et al., 1989. | MR 1002568 | Zbl 0747.05073
- - ,[Br] Groups of type E7, J. reine angew. Math., 236, no. 1 (1969), 79-102. | MR 248185 | Zbl 0182.04703
,[C] Simple groups of Lie type, Wiley, London et al., 1972. | MR 407163 | Zbl 0248.20015
,[CC1] The 2-space of the standard E6(q)-mudule, Geom. dedic., 25, no. 1-3 (1988), pp. 467-480. | MR 925847 | Zbl 0643.20025
- ,[CC2] Gröbner bases and standard monomial theory, Computational algebraic geometry, Progess in Mathematics 109, Birkhäuser, 1993, pp. 41-60. | MR 1230857 | Zbl 0808.13010
- ,[CW] Finite subgroups of F4(C) and E6(C), Proc. London Math. Soc., 74, no. 1 (1997), pp. 105-150. | MR 1416728 | Zbl 0874.20032
- ,[C1] The geometry of root subgroups in exceptional groups, Geom. dedic., 8, no. 3 (1978), pp. 317-381; 15, no. 1 (1983), pp. 1-45. | MR 550374 | Zbl 0536.20010
,[C2] The fifty-six-dimensional module for E 7. A four form for E7, J. Algebra, 173 (1995), pp. 361-389. | MR 1325780 | Zbl 0838.20047
,[C3] Four forms I. Basic concepts and examples (to appear).
,[CIK] Hecke algebras and characters of parabolic type of finite groups with (B, N)- pairs, Publ. Math. Inst. Hautes Et. Sci., no. 40 (1971), pp. 81-116. | Numdam | MR 347996 | Zbl 0254.20004
- - ,[DMV] (2, 3)-generation of E6(q) (to appear).
- ,[FF] Exceptional Lie algebras and related algebraic and geometric structures, Bull. London Math. Soc., 9 (1977), pp. 1-35. | MR 444729 | Zbl 0349.17004
- ,[GS] Some representations of exceptional Lie algebras, Geom. dedic., 25, no. 1-3 (1988), pp. 407-416. | MR 925845 | Zbl 0661.17005
- ,[G] A Moufang loop, the exceptional Jordan algebra and a cubic form in 27 variables, J. Algebra, 13 (1990), pp. 281-293. | MR 1055009 | Zbl 0718.17028
,[HOM] The classical groups and K-theory, Springer-Verlag, N. Y. et al., 1989. | MR 1007302 | Zbl 0683.20033
- ,[Ha] Some irreducible representations of exceptional algebraic groups, Amer. J. Math., 93, no. 1 (1971), pp. 75-106. | MR 279103 | Zbl 0215.39603
,[Hr] Algebraic Geometry, Springer-Verlag, N. Y. et al., 1977. | MR 463157
,[Hé] Groupes de Chevalley et groupes classiques, Publ. Math. Univ. Paris VII, 17 (1984), pp. 1-54. | MR 772212 | Zbl 0583.17005
,[Hi1] Combinatorics and intersections of Schubert varieties, Comment. Math. Helv., 57 (1982), pp. 41-59. | MR 672845 | Zbl 0501.14030
,[Hi1] Geometry of Coxeter groups, Pitman, Boston and London, 1982. | MR 649068 | Zbl 0483.57002
,[Ho] Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, Israel Math. Conf. Proc. (to appear). | MR 1321638 | Zbl 0844.20027
,[H] Introduction to Lie algebras and representation theory, Springer, Berlin et al., 1980. | MR 499562 | Zbl 0254.17004
,[J] Quantum groups and their primitive ideals, Springer-Verlag, N.Y. et al., 1995. | MR 1315966 | Zbl 0808.17004
,[K1] Crystallizing the q-analogue of universal enveloping algebra, Comm. Math. Phys., 133 (1990), pp. 249-260. | MR 1090425 | Zbl 0724.17009
,[K2] On crystal base of q-analogue of universal envoloping algebras, Duke Math. J., 63 (1991), pp. 456-516. | MR 1115118 | Zbl 0739.17005
,[K3] On crystal bases, Canadian Math. Soc. Conf. Proc., 16 (1995), pp. 155-197. | MR 1357199 | Zbl 0851.17014
,[KN] Crystal graphs for representations of the q-analogue of classical Lie algebras, J. Algebra, 165 (1994), pp. 295-345. | MR 1273277 | Zbl 0808.17005
- ,[LS1] Geometry of G/P. V, J. Algebra, 100 (1986), pp. 462-557. | MR 840589 | Zbl 0618.14026
- ,[LS1] Standard monomial theory, Hyderabad Conference on Algebraic Groups, Manoj Prakashan, Madras, 1991, pp. 279-323. | MR 1131317 | Zbl 0785.14028
- ,[LW] Multiplicities of points on a Schubert variety in a minuscule G/P, Adv. Math., 84, no. 2 (1990), pp. 179-208. | MR 1080976 | Zbl 0729.14037
- ,[Li] A system of quadrics describing the orbit of the highest weight vector, Proc. Amer. Math. Soc., 84, no. 4 (1982), pp. 605-608. | MR 643758 | Zbl 0501.22017
,[LS] On the orders of the maximal subgroups of the finite exceptional groupes of Lie type, Proc. London Math. Soc., 55 (1987), pp. 299-330. | MR 896223 | Zbl 0627.20026
- ,[Li1] A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent. Math., 116 (1994), 229-246. | MR 1253196 | Zbl 0805.17019
,[Li2] Crystal graphs and Young tableau, J. Algebra, 175, no. 1 (1995), pp. 65-87. | MR 1338967 | Zbl 0831.17004
,[Li3] Path and root operators in representation theory, Ann. Math., 142 (1995), pp. 499-525. | MR 1356780 | Zbl 0858.17023
,[L1] Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc., 3 (1990), pp. 447-498. | MR 1035415 | Zbl 0703.17008
,[L2] Canonical bases arising from quantized envoloping algebras. II, Progr. Theor. Physics, 102 (1990), pp. 175-202. | MR 1182165 | Zbl 0776.17012
,[L2] Introduction to quantum groups, Birkhäuser, Boston et al., 1993. | MR 1227098 | Zbl 0788.17010
,[Mn] Cubic forms: algebra, geometry, arithmetic, North-Holland, Amsterdam-London, 1974. | MR 833513 | Zbl 0582.14010
,[Mr] Les nombers de Tamagawa de certains groupes exceptionnels, Bull. Soc. Math. France, 94 (1966), pp. 97-140. | Numdam | MR 213363 | Zbl 0146.04601
,[Ma] On the adjoint module of a quantum group, Preprint University Warwick, no. 79 (1994), pp. 1-12.
,[M] Sur les sous-groupes arithmétiques des groupes semisimples deployés, Ann. Sci. Ecole Norm. Sup., 4ème sér., 2 (1969), pp. 1-62. | Numdam | MR 240214 | Zbl 0261.20025
,[MPS] The Demazure-Tits subgroup of a simple Lie group, J. Math. Phys., 29 no. 4 (1988), pp. 777-796. | MR 940338 | Zbl 0661.22007
- - ,[PR] Minuscule Representations, Preprint Universität Bielefeld, no. 72 (1993).
- ,[Pl1] Stability theorems for K1-functors for Chevalley groups, Proc. Conf. Nonassociative algebras and related topics. Hiroshima- 1990, World Scientific, London et al., 1991, pp. 203-217. | MR 1150261 | Zbl 0801.20019
,[Pl2] Surjective stabilization for K1-functors for some exceptional Chevalley groups, J. Soviet Math., 64, no. 1 (1993), pp. 751-767. | MR 1164860 | Zbl 0802.19003
,[Pl3] On a problem of H. Bass for Chevalley groups of type E7, Y. Algebra, 210, no. 1 (1998), pp. 67-85. | Zbl 0918.20039
,[PSV] Visual basic representations: an atlas, Int. J. Algebra and Computations, 8, no. (1998), pp. 61-97. | MR 1492062 | Zbl 0957.17006
- - ,[P1] Bruhat lattices, plane partition generating functions, and minuscule representations, Europ. J. Combinatorics, 5 (1984), pp. 331-350. | MR 782055 | Zbl 0562.05003
,[P2] A Dynkin diagram classification theorem arising from a combinatorial problem, Adv. Math., 62, no. 2 (1986), pp. 103-117. | MR 865833 | Zbl 0639.06006
,[Sch] Buildings, Handbook of Incidence Geometry, North Jolland, Amsterdam, 1995, pp. 477-645. | MR 1360726 | Zbl 0841.51005
,[Se] Geometry of G/P. I. Standard monomial theory for minuscule P, C. P. Ramanujan: a tribute, Tata Press, Bombay, 1978, pp. 207-239. | MR 541023 | Zbl 0447.14010
,[S1] On the geometric algebra of the projective octave plane, Proc. Nederl. Akad. Wetensch., 65 (1962), pp. 451-468. | MR 142045 | Zbl 0113.35903
,[S2] Jordan algebras and algebraic groups, Springer-Verlag, N. Y. et al., 1973. | MR 379618 | Zbl 0259.17003
,[S3] Linear algebraic groups, Fundam. trends in Math., 55 (1989), pp. 5-136 (in Russian, English translation in Springer-Verlag). | MR 1100484 | Zbl 0789.20044
,[St1] Generators, relations and coverings of Chevalley groups over commutative rings, Amer. J. Math., 93, no. 4 (1971), pp. 965-1004. | MR 322073 | Zbl 0246.20034
,[St2] Stability theorems for K1, K 2 and related functors modeled on Chevalley groups, Japan J. Math., 4, no. 1 (1978), pp. 77-108. | MR 528869 | Zbl 0403.18010
,[S] Lectures on Chevalley groups, Yale University, 1968. | MR 466335
,[St] On minuscule representations, plane partitions and involutions in complex Lie groups, Duke J. Math., 73, no. 2 (1994), pp. 469-490. | MR 1262215 | Zbl 0805.22006
,[SV] Decomposition of transvections: a theme with variations, K-theory, 19 (2000), pp. 109-153. | MR 1740757 | Zbl 0944.20031
- ,[Te] A1-type overgroups of elements of order p in semisimple algebraic groups and associated finite groups, J. Algebra, 177, no. 1 (1995), pp. 34-76. | MR 1356359 | Zbl 0857.20025
,[T] Normalisateurs de tores. I. Groupes de Coxeter étendus, J. Algebra, 4, no. 1 (1966), pp. 96-116. | MR 206117 | Zbl 0145.24703
,[V1] On the problem of normality of the elementary subgroup in a Chevalley group, Algebraic and Discrete Systems, Ivanovo Univ., 1988, pp. 7-25 (in Russian). | MR 1244582 | Zbl 0816.20041
,[V2] Structure of Chevalley groups over commutative rings, Proc. Conf. Nonassociative algebras and related topics. Hiroshima- 1990, World Scientific, London et al., 1991, pp. 219-335. | MR 1150262 | Zbl 0799.20042
,[V3] Do it yourself structure constants for Lie algebras of type El, Preprint Universität Bielefeld, no. 35 (1993), pp. 1-42. | Zbl 1062.17004
,[V4] Intermediate subgroups in Chevalley groups, Proc. Conf. Groups of Lie Type and their Geometries (Como - 1993), Cambridge Univ. Press, 1995, pp. 233-280. | MR 1320525 | Zbl 0879.20020
,[V5] The ubiquity of microweights (to appear).
,[V6] Can one see the signs of the structure constants ?, St. Petersburg J. Math. (In Russian, to appear).
,[V7] Geometry of the minimal modules for Chevalley groups of types E6 and E7 (to appear).
,[VPe] Transvections in polyvector representations, St. Petersburg J. Math. (In Russian, to appear).
- ,[VP] Chevalley groups over commutative rings. I. Elementary calculations, Acta Applicandae Math., 45, no. 1 (1996), pp. 73-113. | MR 1409655 | Zbl 0861.20044
- ,[VP] Calculations in Chevalley groups over commutative rings, Soviet Math. Dokl., 40 no. 1 (1989), pp. 145-147. | MR 1020667 | Zbl 0795.20028
- - ,[W] Automorphisms of det(xij): a group scheme approach, Adv. Math., 65, no. 2 (1987), pp. 171-203. | MR 900267 | Zbl 0651.14028
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