Project Euclid

References

• [1] E. ABE, Hopf algebras, Cambridge Tracts in Math. 74, Cambridge Univ. Press, 1980.
  Mathematical Reviews (MathSciNet): MR594432
  Zentralblatt MATH: 0476.16008
  
• [2] K. AKIN AND D. A. BUCHSBAUM, Characteristic-free representation theory of the general linear group, Adv. in Math. 58 (1985), 149-200.
  Mathematical Reviews (MathSciNet): MR814749
  Zentralblatt MATH: 0607.20021
  Digital Object Identifier: doi:10.1016/0001-8708(85)90115-X
  
• [3] K. AKIN AND D. A. BUCHSBAUM, Characteristic-free representation theory of the general linear grou II Homological considerations, Adv. in Math. 72 (1988), 171-210.
  Mathematical Reviews (MathSciNet): MR972760
  Zentralblatt MATH: 0681.20028
  Digital Object Identifier: doi:10.1016/0001-8708(88)90027-8
  
• [4] K. AKIN, D. A. BUCHSBAUM AND J. WEYMAN, Schur functors and Schur comlexes, Adv. in Math. 4 (1982), 207-278.
  Mathematical Reviews (MathSciNet): MR658729
  Zentralblatt MATH: 0497.15020
  Digital Object Identifier: doi:10.1016/0001-8708(82)90039-1
  
• [5] G. M. BERGMAN, The diamond lemma for ring theory, Adv. in Math. 29 (1978), 178-218
  Mathematical Reviews (MathSciNet): MR506890
  Zentralblatt MATH: 0377.16013
  Digital Object Identifier: doi:10.1016/0001-8708(78)90010-5
  
• [6] C. CURTIS AND I. REINER, Representation theory of finite groups and associative algebras, Pure an Appl. Math., vol. 11, Interscience, New York, 1962; 2nd ed., 1966.
  Mathematical Reviews (MathSciNet): MR144979
  Zentralblatt MATH: 0131.25601
  
• [7] V. G. DRIN'FELD, Quantum groups, Proc. ICM, Berkeley, 1986
  Mathematical Reviews (MathSciNet): MR934283
  
• [8] E. DATE, M. Jimbo and T. Miwa, Representations of Uq(Q(n, C)) at g =0 and the Robinson-Shenste correspondence, Memorial Volume for Vadim Kniznik, Physics and Mathematics of Strings, World Scientific, Singapore, 1990, 185-211.
  Mathematical Reviews (MathSciNet): MR1104259
  Zentralblatt MATH: 0743.17018
  
• [9] P. DELIGNE AND J. MILNE, Tannakian categories, Lecture Notes in Math. 900, Springer-Verlag, Berli Heidelberg New York, 1982, 101-228.
  Zentralblatt MATH: 0477.14004
  
• [10] R. DIPPER AND G. JAMES, ^-tensor space and #-Weyl modules, preprint
• [11] P. DOUBILET, G. -C. ROTA AND J. STEIN, Foundations of combinatorics. IX. Combinatorial method in invariant theory, Stud. Appl. Math. 43 (1971), 1020-1058.
• [12] L. D. FADDEEV, N. Yu. RESHETIKHIN AND L. A. TAKHTAJAN, Quantization of Lie groups and Li algebras, Algebra and Analysis 1 (1989), 178-206 (English translation: Leningrad Math. J. 1 (1990), 193-225).
  Mathematical Reviews (MathSciNet): MR1015339
  Zentralblatt MATH: 0715.17015
  
• [13] J. A. GREEN, Polynomial representations of GLn, Lecture Notes in Math. 830, Springer-Verlag, Berli Heidelberg New York, 1980.
  Mathematical Reviews (MathSciNet): MR606556
  Zentralblatt MATH: 0451.20037
  
• [14] A. GYOJA, A ^-analogue of Young symmetrizer, Osaka J. Math. 23 (1986), 841-852
  Mathematical Reviews (MathSciNet): MR873212
  Zentralblatt MATH: 0644.20012
  Project Euclid: euclid.ojm/1200779724
  
• [15] A. GYOJA AND K. UNO, On the semisimplicity of Hecke algebras, J. Math. Soc. Japan 41 (1989), 75-79
  Mathematical Reviews (MathSciNet): MR972165
  Zentralblatt MATH: 0647.20038
  Digital Object Identifier: doi:10.2969/jmsj/04110075
  Project Euclid: euclid.jmsj/1230128847
  
• [16] T. HIBI, Distributive lattices, affine semigroup rings and algebras with straightening laws, in Advance Studies in Pure Math. 11, Kinokuniya, Tokyo and North-Holland, Amsterdam, 1987, 93-109.
  Mathematical Reviews (MathSciNet): MR951198
  Zentralblatt MATH: 0654.13015
  
• [17] T. HAYASHI, Quantum deformation of classical groups, Publ. Res. Inst, Math. Sci., Kyoto Univ. 2 (1992), 57-81.
  Mathematical Reviews (MathSciNet): MR1147851
  Zentralblatt MATH: 0806.16040
  Digital Object Identifier: doi:10.2977/prims/1195168856
  
• [18] M. JIMBO, A ^-difference analogue of t/(g) and the Yang-Baxter equation, Lett, in Math. Phys. 1 (1985), 63-69.
  Mathematical Reviews (MathSciNet): MR797001
  Zentralblatt MATH: 0587.17004
  Digital Object Identifier: doi:10.1007/BF00704588
  
• [19] M. JIMBO, Quantum R matrix related to the generalized Toda system: an algebraic approach, Lectur Notes in Phys. 246, Springer-Verlag, Berlin Heidelberg New York, 1986, 335-361.
  Mathematical Reviews (MathSciNet): MR848629
  Digital Object Identifier: doi:10.1007/3-540-16452-9_21
  
• [20] M. JIMBO, A ^-analogue of t/(gl(7V-f 1)), Hecke algebra and the Yang-Baxter equation, Lett, in Math Phys. 11 (1986), 247-252.
  Mathematical Reviews (MathSciNet): MR841713
  Zentralblatt MATH: 0602.17005
  Digital Object Identifier: doi:10.1007/BF00400222
  
• [21] P. P. KULISH, N. Yu. RESHETIKHIN AND E. K. SKLYANIN, Yang-Baxter equation and representatio theory. I, Lett. Math. Phys. 5 (1981), 393-403.
  Mathematical Reviews (MathSciNet): MR649704
  Zentralblatt MATH: 0502.35074
  Digital Object Identifier: doi:10.1007/BF02285311
  
• [22] P. P. KULISH AND E. K. SKLYANIN, Quantum spectral transform method. Recent developments, Integrable quantum field theories, Lecture Notes in Physics 151, Springer-Verlag, Berlin Heidelberg New York, 1981, 61-119.
  Mathematical Reviews (MathSciNet): MR671263
  Zentralblatt MATH: 0734.35071
  
• [23] G. LUSZTIG, Modular representations and quantum groups, Contemp. Math. 82, Amer. Math. Soc., Providence, R. I., 1989, 59-77.
  Mathematical Reviews (MathSciNet): MR982278
  Zentralblatt MATH: 0665.20022
  
• [24] V. V. LYUBASHENKO, Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-18 (in Russian).
  Mathematical Reviews (MathSciNet): MR878344
  Zentralblatt MATH: 0649.16008
  
• [25] I. G. MACDONALD, Symmetric functions and Hall polynomials, Oxford Univ. Press, 1979
  Mathematical Reviews (MathSciNet): MR553598
  Zentralblatt MATH: 0487.20007
  
• [26] Yu. I. MANIN, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier, Grenobl 37 (1987), 191-205.
  Mathematical Reviews (MathSciNet): MR927397
  Zentralblatt MATH: 0625.58040
  
• [27] Yu. I. MANIN, Multiparametric quantum deformation of the general linear supergroup, Commun Math. Phys. 123 (1989), 163-175.
  Mathematical Reviews (MathSciNet): MR1002037
  Zentralblatt MATH: 0673.16004
  Digital Object Identifier: doi:10.1007/BF01244022
  Project Euclid: euclid.cmp/1104178686
  
• [28] D. G. NORTHCOTT, Multilinear algebra, Cambridge University Press, 1984
  Mathematical Reviews (MathSciNet): MR773853
  Zentralblatt MATH: 0543.15019
  
• [29] M. NOUMI, H. YAMADA AND K. MIMACHI, Finite dimensional representations of the quantum grou GLq(n) and the zonal spherical functions on Uq(n– l)\Uq(n), preprint.
• [30] B. PARSHALL AND J. WANG, Quantum linear groups, Memoirs of the Amer. Math. Soc. 439 (1991)
  Mathematical Reviews (MathSciNet): MR1048073
  
• [31] P. PODLES, Quantum spheres, Lett, in Math. Phys. 14 (1987), 193-202
  Mathematical Reviews (MathSciNet): MR919322
  Zentralblatt MATH: 0634.46054
  Digital Object Identifier: doi:10.1007/BF00416848
  
• [32] S. B. PRIDDY, Koszul resolutions, Trans. Amer. Math. Soc. 152-1 (1970), 39-60
  Mathematical Reviews (MathSciNet): MR265437
  Zentralblatt MATH: 0261.18016
  Digital Object Identifier: doi:10.2307/1995637
  JSTOR: links.jstor.org
  
• [33] N. Yu. RESHETIKHIN, Quantum universalenvelopingalgebras, the Yang-Baxter equation and invariant of links. I, preprint.
• [34] M. SWEEDLER, Hopf algebras, W. A. Benjamin, New York, 1969
  Mathematical Reviews (MathSciNet): MR252485
  Zentralblatt MATH: 0194.32901
  
• [35] M. TAKEUCHI, Matric bialgebras and quantum groups, Israel J. of Math. 72 (1990), 232-251
  Mathematical Reviews (MathSciNet): MR1098990
  Zentralblatt MATH: 0723.17013
  Digital Object Identifier: doi:10.1007/BF02764621
  
• [36] T. TANISAKI, Finite dimensional representations of quantum groups, Osaka J. of Math. 28(1991), 37-54
  Mathematical Reviews (MathSciNet): MR1096926
  Zentralblatt MATH: 0729.17008
  Project Euclid: euclid.ojm/1200782857
  
• [37] E. TAFT AND J. TOWBER, Quantum deformation of flag schemes and Grassmann schemes I ^-deformation of the shape-algebra for GL(n), J. Algebra 142 (1991), 1-36.
  Mathematical Reviews (MathSciNet): MR1125202
  Zentralblatt MATH: 0739.17007
  Digital Object Identifier: doi:10.1016/0021-8693(91)90214-S
  
• [38] V. G. TURAEV, The Yang-Baxter equation and invariant of links, Invent. Math. 92 (1988), 527-553
  Mathematical Reviews (MathSciNet): MR939474
  Zentralblatt MATH: 0648.57003
  Digital Object Identifier: doi:10.1007/BF01393746
  
• [39] K. UENO, T. Takebayashi, Y. Shibukawa, Gelfand-Tsetlin basis for representations of the quantu group GLq(N+ 1) and the basic quantum affine space, preprint.
• [40] S. L. WORONOWICZ, Compact matrix pseudogroups, Comm. Math. Phys. III (1987), 613-665
  Mathematical Reviews (MathSciNet): MR901157
  Zentralblatt MATH: 0627.58034
  Digital Object Identifier: doi:10.1007/BF01219077
  Project Euclid: euclid.cmp/1104159726