On infinite-dimensional grassmannians and their quantum deformations

R. Fioresi; C. Hacon

Rendiconti del Seminario Matematico della Università di Padova (2004)

  • Volume: 111, page 1-24
  • ISSN: 0041-8994

How to cite

top

Fioresi, R., and Hacon, C.. "On infinite-dimensional grassmannians and their quantum deformations." Rendiconti del Seminario Matematico della Università di Padova 111 (2004): 1-24. <http://eudml.org/doc/108627>.

@article{Fioresi2004,
author = {Fioresi, R., Hacon, C.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {1-24},
publisher = {Seminario Matematico of the University of Padua},
title = {On infinite-dimensional grassmannians and their quantum deformations},
url = {http://eudml.org/doc/108627},
volume = {111},
year = {2004},
}

TY - JOUR
AU - Fioresi, R.
AU - Hacon, C.
TI - On infinite-dimensional grassmannians and their quantum deformations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2004
PB - Seminario Matematico of the University of Padua
VL - 111
SP - 1
EP - 24
LA - eng
UR - http://eudml.org/doc/108627
ER -

References

top
  1. [A] E. ABE, Hopf Algebras, Cambridge University Press, Cambridge, MA, 1980. Zbl0476.16008MR594432
  2. [CP] V. CHARI - A. PRESSLEY, A guide to quantum groups, Cambridge Press, 1994. Zbl0839.17009MR1300632
  3. [FRT] L. D. FADDEEV - N. Y. RESHETIKHIN - L. A. TAKHTAJAN, Quantization of Lie groups and Lie algebras, Algebraic analysis, Vol. I, pp. 129-139, Academic Press, Boston, MA, 1988. Zbl0677.17010MR992450
  4. [Fi1] R. FIORESI, Quantization of the grassmannian manifold, J. Algebra, 214, no. 2 (1999), pp. 418-447. Zbl0955.17007MR1680557
  5. [Fi2] R. FIORESI, Quantum deformation of the flag manifold, Comm. Alg., 27, no. 11 (1999), pp. 5669-5685. Zbl0955.17008MR1713061
  6. [FH] R. FIORESI - C. HACON, Quantum coinvariant theory and quantum Schubert manifolds, preprint, 1999. 
  7. [Fu] W. FULTON, Young Tableaux, Cambridge University Press, Cambridge, 1997. Zbl0878.14034MR1464693
  8. [GH] P. GRIFFITHS - J. HARRIS, Principles of algebraic geometry, Wiley and Sons, New York, 1978. Zbl0408.14001MR507725
  9. [Ka] V. KAC - A. K. RAINA, Bombay Lecture notes on weight representations of infinite-dimensional Lie algebras, Advanced Series in Mathematical Physics, World Scientific Publishing, 1987. Zbl0668.17012MR1021978
  10. [Ku] S. KUMAR, Infinite grassmannians and moduli spaces of G-bundles, Lecture Notes in Mathematics, 1649, pp. 1-49, Springer, 1997. Zbl0884.14021MR1605027
  11. [La] S. LANG, Hilbert’s Nullstellensatz in infinite dimensional space, Proc. Amer. Math. Soc., 3 (1952), 407-410. Zbl0049.30405MR47019
  12. [LR] V. LAKSHMIBAI - N. RESHETIKHIN, Quantum flag and Schubert schemes (Amherst, MA, 1990), pp. 145-181, Contemp. Math., 134, Amer. Math. Soc., Providence, RI, 1992. Zbl0792.17012MR1187287
  13. [Ma1] Y. I. MANIN, Quantum groups and non commutative geometry, Centre de Reserches Mathematiques Montreal, 49, 1988. Zbl0724.17006MR1016381
  14. [Ma2] Y. I. MANIN, Topics in noncommutative geometry, M. B. Porter Lectures, Princeton University Press, Princeton, NJ, 1991. Zbl0724.17007MR1095783
  15. [Mu1] M. MULASE, A correspondence between an infinite-dimensional grassmannian and arbitrary vector bundles on algebraic curves, Proceedings of Symposia in Pure Mathematics, 49, Part I, Amer. Math. Soc., Providence RI, 1989. Zbl0676.58010MR1013124
  16. [Mu2] M. MULASE, Category of vector bundles on algebraic curves on infinitedimensional grassmannians, Int. J. Math, 1, no. 3 (1990), 293-342. Zbl0723.14010MR1078516
  17. [PW] B. PARSHALL - J. P. WANG, Quantum linear groups, Mem. Amer. Math. Soc., 89, no. 439, 1991. Zbl0724.17011MR1048073
  18. [PM] F. PLAZA MARTIN, Grassmannian of k((z)): Picard group equations and automorphisms, preprint, 1998. Zbl1006.14019MR1794521
  19. [PS] A. PRESSLEY - G. SEGAL, Loop Groups, Cambridge Press, 1991. Zbl0618.22011MR1071737
  20. [Sa1] M. SATO, Soliton equations as dynamical systems on an infinite-dimensional grassmannian manifold, Kokyoroku, RIMS, Kyoto University, 439 (1981), 30-46. Zbl0507.58029
  21. [Sa2] M. SATO, The KP hierarchy and infinite-dimensional grassmannian manifold, Proceedings of Symposia in Pure Mathematics, 49, Part I, Amer. Math. Soc., Providence RI, 1989. Zbl0688.58016MR1013125
  22. [SW] G. SEGAL - G. WILSON, Loop groups and equations of KdV type, Publ. Math. IHES, 61 (1985), pp. 5-65. Zbl0592.35112MR783348
  23. [So] Y. S. SOIBELMAN, On the quantum flag manifold (Russian) Funktsional. Anal. i Prilozhen., 26, no. 3 (1992), pp. 90-92; translation in Functional Anal. Appl., 26, no. 3 (1992), pp. 225-227. Zbl0820.17017MR1189033
  24. [TT] E. TAFT - J. TOWBER, Quantum deformation of flag schemes and Grassmann schemes, I. A q-deformation of the shape-algebra for GL(n), J. Algebra, 142, no. 1 (1991), pp. 1-36. Zbl0739.17007MR1125202
  25. [VS] L. L. VAKSMAN - Y. S. SOIBELMAN, On some problems in the theory of quantum groups, Representation theory and dynamical systems, 3-55, Adv. Soviet Math., 9, Amer. Math. Soc., Providence, RI, 1992. Zbl0766.58007MR1166194
  26. [W] E. WITTEN, Quantum Field Theory, Grassmannians and algebraic curves, Comm. Math. Phys., 113 (1988), pp. 529-600. Zbl0636.22012MR923632

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.