Dirac operators on quantum flag manifolds

Letters in Mathematical Physics

Volumn 67, Issue 1, 2004, Pages 49-59

  Krähmer, Ulrich ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Noncommutative geometry; Quantum homogeneous spaces

Indexed keywords

EID: 3943061537     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MATH.0000027748.64886.23     Document Type: Article

References (20)

1. Baston, R. J. and Eastwood, M. G.: The Penrose Transform, Oxford University Press, 1989.
2. 2q-1(C), Lett. Math. Phys. 18 (1989), 165-176.
3. Cahen, M. and Gutt, S.: Spin structures on compact simply connected Riemannian symmetric spaces, Simon Stevin 62(3/4) (1988), 209-242.
4. Chakraborty, P. S. and Pal, A.: Equivariant spectral Triples on the quantum SU(2) group, K-Theory 28(2) (2003), 107-126.
5. Connes, A.: Noncommutative Geometry, Academic Press, New York, 1994.
6. q(2), math.QA/0209142.
7. Däbrowski, L. and Sitarz, A.: Dirac operator on the standard Podleś' quantum sphere. In: Noncommutative Geometry and Quantum Groups, Banach Center Publications 61 (2003), 49-58.
8. Dijkhuizen, M. S. and Stokman, J. V.: Quantized flag manifolds and irreducible *-representations, Comm. Math. Phys. 203 (1999), 297-324.
9. Friedrich, T.: Dirac Operators in Riemannian Geometry. Amer. Math. Soc., Providence, 2000.
10. Fulton, W. and Harris, J.: Representation Theory, Springer, New York, 1991.
11. Goswami, D.: Twisted entire cyclic cohomology, J-L-O cocycles and equivariant spectral triples. math-ph/0204010.
12. Gover, A. R. and Zhang, R. B.: Geometry of quantum homogeneous vector bundles and representation theory of quantum groups I, Rev. Math. Phys. 11(5) (1999), 533-552.
13. Heckenberger, I. and Kolb, S.: The locally finite part of the dual coalgebra of quantized irreducible flag manifolds, math.QA/0301244, to appear in Proc. London Math. Soc.
14. Heckenberger, I. and Kolb, S.: Differential calculus on quantum homogeneous spaces, Lett. Math. Phys. 63(3) (2003), 255-264.
15. Joseph, A.: Quantum Groups and their Primitive Ideals. Springer, New York, 1995.
16. Klimyk, A. U. and Schmüdgen, K.: Quantum Groups and their Representations, Springer, New York, 1997.
17. Parthasarathy, R.: Dirac operator and the discrete series, Ann. of Math. 96(2) (1972), 1-30.
18. Podleś, P.: Quantum spheres, Lett. Math. Phys. 14 (1987), 193-202.
19. q(2). J. Geom. Phys. 31 (1999), 241-264.
20. Woronowicz, S. L.: Differential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122(1) (1989), 125-170.