New branching rules induced by plethysm

Journal of Physics A: Mathematical and General

Volumn 39, Issue 11, 2006, Pages 2611-2655

  Fauser, B ^a   Jarvis, P D ^b   King, R C ^c   Wybourne, B G ^d  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF TASMANIA   (Australia)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^d NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644640671     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/11/006     Document Type: Article

References (43)

1. Abłamowicz R and Fauser B 2005 Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple Comput. Phys. Commun. 170 115-30
2. Barcelo H and Ram A 1999 Combinatorial Representation Theory (Math. Sci. Res. Inst. Publ. 38) (Cambridge, Berkeley, CA: Cambridge University Press) pp 23-90
3. Black G R E, King R C and Wybourne B G 1983 Kronecker products for compact semisimple Lie groups J. Phys. A: Math. Gen. 16 1555-89
4. Brouder C, Fauser B, Frabetti A and Oeckl R 2004 Quantum field theory and Hopf algebra cohomology [formerly 'Let's twist again'] J. Phys. A: Math. Gen. 37 5895-927 (Preprint hep-th/0311253)
5. Brouder C, Frabetti A and Krattenthaler C 2004 Non-commutative Hopf algebra of formal diffeomorphisms p 33 Preprint math.QA/0406117
6. Brouder C and Schmitt W 2002 Quantum groups and quantum field theory III. Renormalization pp 1-18 Preprint hep-th/0210097
7. Carvalho M J and D'Agostino S 2001 Plethysm of Schur functions and the shell model J. Phys. A: Math. Gen. 1375-92
8. Carvalho M J and D'Agostino S 2001 A MAPLE program for calculations with Schur functions Comput. Phys. Commun. 141 282-95
9. Dubois-Violette M and Henneaux M 2002 Tensor fields of mixed Young symmetry type and n-complexes Commun. Math. Phys. 226 393-418
10. Fauser B 2002 A treatise on quantum Clifford algebras. Konstanz. Habilitationsschrift Preprint math.QA/0202059
11. Fauser B and Jarvis P D 2004 A Hopf laboratory for symmetric functions J. Phys. A: Math. Gen: 37 1633-63 (Preprint math-ph/0308043)
12. Fauser B and Jarvis P D 2006 The Hopf algebra of plethysm in preparation
13. Geissinger L 1977 Hopf Algebras of Symmetric Functions and Class Functions (Springer Lecture Notes) vol 579 pp 168-81
14. Hasse R W and Johnson N F 1993 Classification of N-electron states in a quantum dot Phys. Rev. B 48 1583-1594
15. Kassel C 1995 Quantum Groups (New York: Springer)
16. King R C 1971 Modification rules and products of irreducible representations of the unitary, orthogonal, and symplectic groups J. Phys. A: Math. Gen. 12 1588-98
17. King R C 1975 Branching rules for classical Lie groups using tensor and spinor methods J. Phys. A: Math. Gen. 8 429-49
18. King R C, Dehuai L and Wybourne B G 1981 Symmetrized powers of rotation group representations J. Phys. A: Math. Gen. 14 2509-38
19. King R C and Wybourne B G 2002 Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of : I. Characters and products J. Phys. A: Math. Gen. 41 5002-19
20. King R C and Wybourne B G 2002 Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of : II. Plethysms J. Phys. A: Math. Gen. 41 5656-90
21. King R C and Wybourne B G 1985 Holomorphic discrete series and harmonic series unitary irreducible representations of non-compact Lie groups: Sp(2n, R), U(p, q) and SO*(2n) J. Phys. A: Math. Gen. 18 3113-39
22. Knutson D 1973 λ-Rings and the Representation Theory of the Symmetric Group (Berlin: Springer) Lecture Notes in Mathematics 308
23. Kuperberg G 1991 Involutory Hopf algebras and 3-manifold invariants Int. J. Math. 2 41-66
24. Kuperberg G 1996 Noninvolutory Hopf algebras and 3-manifold invariants Duke Math. J. 84 83-129
25. Littlewood D E 1940 The Theory of Group Characters (Oxford: Oxford University Press)
26. Littlewood D E 1950 University Algebra (London: Heinemann)
27. Littlewood D E 1958 The Theory of Group Characters 2nd edn (Oxford: Oxford University Press)
28. Littlewood D E 1958 Products and plethysms of characters with orthogonal, symplectic and symmetric groups Can. J. Math. 10 17-32
29. Littlewood D E 1958 The inner plethysm of S-functions Can. J. Math. 10 1-16
30. Lyubashenko V 1995 Modular transformations for tensor categories J. Pure Appl. Algebra 98 279-327
31. Lyubashenko V 1995 Tangles and Hopf algebras in braided categories J. Pure Appl. Algebra 98 245-78
32. Macdonald I G 1979 Symmetric Functions and Hall Polynomials (Oxford: Clarendon) (1995 2nd edn)
33. Majid S 1995 Foundations of Quantum Group Theory (Cambridge: Cambridge University Press)
34. Scharf T and Thibon J-Y 1994 A Hopf algebra approach to inner plethysm Adv. Math. 104 30-58
35. Sweedler M E 1968 Cohomology of algebras over Hopf algebras Trans. Am. Math. Soc. 133 205-39
36. Thibon J-Y 1991 Coproduits de fonctions symétrique C. R. Acad. Sci., Paris I 312 553-6
37. Thibon J-Y 1991 Hopf algebras of symmetric functions and tensor products of symmetric group representations Int. J. Algebra Comput. 1 2007-221
38. Weyl H 1930 The classical groups, their invariants and representations by Hermann Weyl (Princeton, NJ: Princeton University Press) (1946 2nd edn, with supplement)
39. Wybourne B G et al 2004 http://smc.vnet.net/schur.html SCHUR©, Schur Group Theory Software
40. Yang M and Wybourne B G 1986 New S function series and non-compact Lie groups J. Phys. A: Math. Gen. 19 3513-25
41. Yetter D N 1990 Quantum groups and representations of monoidal categories Math. Proc. Camb. Phil. Soc. 108 261-90
42. Zelevinsky A V 1981 Representations of Finite Classical Groups: A Hopf Algebra Approach (LNM 869) (Berlin: Springer)
43. Zelevinsky A V 1981 A generalization of the Littlewood-Richardson rule and the Robinson-Schensted-Knuth correspondence J. Algebra 69 82-94