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Volumn 15, Issue 1, 2006, Pages 7-19

On the computation of clebsch–gordan coefficients and the dilation effect

Author keywords

Clebsch Gordan coefficients; Computational representation theory; Littlewood Richardson coefficients; Saturation theorem; Tensor product multiplications

Indexed keywords


EID: 33745650320     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2006.10128948     Document Type: Article
Times cited : (49)

References (41)
  • 1
    • 85023916710 scopus 로고    scopus 로고
    • Volume Computation for Polytopes and Partition Functions for Classical Root Systems
    • arXiv: math. CO/0504231
    • M. W. Baldoni, M. Beck, C. Cochet, and M. Vergne. “Volume Computation for Polytopes and Partition Functions for Classical Root Systems.” To appear in Discrete Comp. Geom., arXiv: math. CO/0504231 (2005).
    • (2005) To Appear in Discrete Comp. Geom
    • Baldoni, M.W.1    Beck, M.2    Cochet, C.3    Vergne, M.4
  • 2
    • 0000975439 scopus 로고
    • A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
    • A. I. Barvinok. “A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed.” Math. Oper. Res. 19: 4 (1994), 769–779.
    • (1994) Math. Oper. Res. , vol.19 , Issue.4 , pp. 769-779
    • Barvinok, A.I.1
  • 4
    • 0005186432 scopus 로고
    • Involutions on Gel _ fand–Tsetlin Schemes and Multiplicities in Skew GLn-modules
    • A. D. Berenstein and A. V. Zelevinsky. “Involutions on Gel _ fand–Tsetlin Schemes and Multiplicities in Skew GLn-modules.” Dokl. Akad. Nauk SSSR 300: 6 (1988), 1291–1294.
    • (1988) Dokl. Akad. Nauk SSSR , vol.300 , Issue.6 , pp. 1291-1294
    • Berenstein, A.D.1    Zelevinsky, A.V.2
  • 5
    • 0000764591 scopus 로고
    • Tensor Product Multiplicities and Convex Polytopes in Partition Space
    • A. D. Berenstein and A. V. Zelevinsky. “Tensor Product Multiplicities and Convex Polytopes in Partition Space.” J. Geom. Phys. 5: 3 (1988), 453–472.
    • (1988) J. Geom. Phys. , vol.5 , Issue.3 , pp. 453-472
    • Berenstein, A.D.1    Zelevinsky, A.V.2
  • 6
    • 0035585392 scopus 로고    scopus 로고
    • Tensor Product Multiplicities, Canonical Bases and Totally Positive Varieties
    • A. D. Berenstein and A. V. Zelevinsky. “Tensor Product Multiplicities, Canonical Bases and Totally Positive Varieties.” Invent. Math. 143: 1 (2001), 77–128.
    • (2001) Invent. Math. , vol.143 , Issue.1 , pp. 77-128
    • Berenstein, A.D.1    Zelevinsky, A.V.2
  • 7
    • 0002438119 scopus 로고    scopus 로고
    • The Saturation Conjecture (After A. Knutson and T. Tao)
    • A. S. Buch. “The Saturation Conjecture (after A. Knutson and T. Tao).” Enseign. Math. (2) 46: 1-2 (2000), 43–60.
    • (2000) Enseign. Math. (2) , vol.46 , Issue.1-2 , pp. 43-60
    • Buch, A.S.1
  • 9
    • 0030564733 scopus 로고    scopus 로고
    • Lie Algebraic Computation
    • A. M. Cohen and W. A. de Graaf. “Lie Algebraic Computation.” Comput. Phys. Comm. 97: 1-2 (1996), 53–62.
    • (1996) Comput. Phys. Comm , vol.97 , Issue.1-2 , pp. 53-62
    • Cohen, A.M.1    De Graaf, W.A.2
  • 11
    • 4344582797 scopus 로고    scopus 로고
    • Effective Lattice Point Counting in Rational Convex Polytopes
    • J. A. De Loera, R. Hemmecke, J. Tauzer, and R. Yoshida. “Effective Lattice Point Counting in Rational Convex Polytopes.” J. Symbolic Comput. 38: 4 (2004), 1273–1302.
    • (2004) J. Symbolic Comput. , vol.38 , Issue.4 , pp. 1273-1302
    • De Loera, J.A.1    Hemmecke, R.2    Tauzer, J.3    Yoshida, R.4
  • 12
    • 0037107150 scopus 로고    scopus 로고
    • On the Littlewood–Richardson Polynomials
    • H. Derksen and J. Weyman. “On the Littlewood–Richardson Polynomials.” J. Algebra 255: 2 (2002), 247–257.
    • (2002) J. Algebra , vol.255 , Issue.2 , pp. 247-257
    • Derksen, H.1    Weyman, J.2
  • 13
    • 4344650688 scopus 로고
    • Polynômes arithmétiques et méthode des polyèdres en combinatoire
    • Basel: Birkh¨auser Verlag
    • E. Ehrhart. Polynômes arithmétiques et méthode des polyèdres en combinatoire. International Series of Numerical Mathematics, 35. Basel: Birkh¨auser Verlag, 1977.
    • (1977) International Series of Numerical Mathematics , vol.35
    • Ehrhart, E.1
  • 16
    • 0000834650 scopus 로고
    • Finite-Dimensional Representations of the Group of Unimodular Matrices
    • I. M. Gelfand and M. L. Tsetlin. “Finite-Dimensional Representations of the Group of Unimodular Matrices.” Doklady Akad. Nauk SSSR (N.S.) 71 (1950), 825–828.
    • (1950) Doklady Akad. Nauk SSSR (N.S.) , vol.71 , pp. 825-828
    • Gelfand, I.M.1    Tsetlin, M.L.2
  • 17
    • 0003198090 scopus 로고
    • Introduction to Lie Algebras and Representation Theory
    • New York: Springer-Verlag
    • J. E. Humphreys. Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, 9. New York: Springer-Verlag, 1972.
    • (1972) Graduate Texts in Mathematics , vol.9
    • Humphreys, J.E.1
  • 20
    • 85023908304 scopus 로고    scopus 로고
    • A Path Model for Geodesics in Euclidean Buildings and Its Applications to Representation Theory
    • arXiv: math. RT/0411182
    • M. Kapovich and J. J. Millson. “A Path Model for Geodesics in Euclidean Buildings and Its Applications to Representation Theory.” To appear in Mem. Amer. Math. Soc., arXiv: math. RT/0411182 (2004).
    • (2004) To Appear in Mem. Amer. Math. Soc
    • Kapovich, M.1    Millson, J.J.2
  • 21
    • 34249963938 scopus 로고
    • Crystalizing the q-Analogue of Universal Enveloping Algebras
    • M. Kashiwara. “Crystalizing the q-Analogue of Universal Enveloping Algebras.” Comm. Math. Phys. 133: 2 (1990), 249–260.
    • (1990) Comm. Math. Phys. , vol.133 , Issue.2 , pp. 249-260
    • Kashiwara, M.1
  • 22
    • 12144264589 scopus 로고    scopus 로고
    • Stretched Littlewood–Richardson and Kostka Coefficients
    • Providence: Amer. Math. Soc
    • R. C. King, C. Tollu, and F. Toumazet. “Stretched Littlewood–Richardson and Kostka Coefficients.” In Symmetry in Physics, CRM Proc. Lecture Notes, 34, pp. 99–112. Providence: Amer. Math. Soc., 2004.
    • (2004) Symmetry in Physics, CRM Proc. Lecture Notes , vol.34 , pp. 99-112
    • King, R.C.1    Tollu, C.2    Toumazet, F.3
  • 23
    • 3242741349 scopus 로고    scopus 로고
    • Ubiquity of Kostka Polynomials
    • River Edge, NJ: World Sci. Publishing
    • A. N. Kirillov. “Ubiquity of Kostka Polynomials.” In Physics and Combinatorics 1999 (Nagoya), pp. 85–200. River Edge, NJ: World Sci. Publishing, 2001.
    • (2001) Physics and Combinatorics 1999 (Nagoya) , pp. 85-200
    • Kirillov, A.N.1
  • 25
    • 0033423661 scopus 로고    scopus 로고
    • n(C) Tensor Products I: Proof of the Saturation Conjecture
    • n(C) Tensor Products I: Proof of the Saturation Conjecture.” J. Amer. Math. Soc. 12: 4 (1999), 1055–1090.
    • (1999) J. Amer. Math. Soc. , vol.12 , Issue.4 , pp. 1055-1090
    • Knutson, A.1    Tao, T.2
  • 26
    • 5344237452 scopus 로고    scopus 로고
    • A Positive Proof of the Littlewood–Richardson Rule Using the Octahedron Recurrence
    • Research paper 61, 18 pp
    • A. Knutson, T. Tao, and C. Woodward. “A Positive Proof of the Littlewood–Richardson Rule Using the Octahedron Recurrence.” Electron. J. Combin. 11 (2004), Research paper 61, 18 pp.
    • (2004) Electron. J. Combin , vol.11
    • Knutson, A.1    Tao, T.2    Woodward, C.3
  • 27
    • 0040045793 scopus 로고
    • LIE, A Software Package for Lie Group Computations
    • M. A. A. van Leeuwen. “LIE, A Software Package for Lie Group Computations.” Euromath Bull. 1: 2 (1994) 83–94. Software and manual available at http: //wwwmathlabo.univ-poitiers.fr/∼maavl/LiE/.
    • (1994) Euromath Bull , vol.1 , Issue.2 , pp. 83-94
    • Van Leeuwen, M.A.A.1
  • 28
    • 0041177574 scopus 로고    scopus 로고
    • Cones, Crystals, and Patterns
    • P. Littelmann. “Cones, Crystals, and Patterns.” Transform. Groups 3: 2 (1998), 145–179.
    • (1998) Transform. Groups , vol.3 , Issue.2 , pp. 145-179
    • Littelmann, P.1
  • 29
    • 85023924194 scopus 로고    scopus 로고
    • Maplesoft. “Maple.” Available at http: //www. maplesoft.com/.
    • Maple
  • 30
    • 33745678445 scopus 로고    scopus 로고
    • Geometric Complexity Theory, P vs. NP and Explicit Obstructions
    • New Delhi: Hindustan Book Agency
    • K. Mulmuley and M. Sohoni. “Geometric Complexity Theory, P vs. NP and Explicit Obstructions.” In Advances in Algebra and Geometry (Hyderabad, 2001), pp. 239–261. New Delhi: Hindustan Book Agency, 2003.
    • (2003) Advances in Algebra and Geometry (Hyderabad, 2001) , pp. 239-261
    • Mulmuley, K.1    Sohoni, M.2
  • 31
    • 85039340200 scopus 로고    scopus 로고
    • The Computation of Kostka Numbers and Littlewood–Richardson Coefficients is #P-complete
    • arXiv: math. CO/0501176
    • H. Narayanan. “The Computation of Kostka Numbers and Littlewood–Richardson Coefficients is #P-complete.” To appear in J. Algebraic Combin., arXiv: math. CO/0501176 (2005).
    • (2005) To Appear in J. Algebraic Combin
    • Narayanan, H.1
  • 32
    • 14644406886 scopus 로고    scopus 로고
    • Combinatorics and Geometry of Littlewood–Richardson Cones
    • I. Pak and E. Vallejo. “Combinatorics and Geometry of Littlewood–Richardson Cones.” Europ. J. Combinatorics. 26 (2005), 995–1008.
    • (2005) Europ. J. Combinatorics. , vol.26 , pp. 995-1008
    • Pak, I.1    Vallejo, E.2
  • 33
    • 4644258912 scopus 로고    scopus 로고
    • TOPCOM: Triangulations of Point Configurations and Oriented Matroids
    • River Edge, NJ: World Sci. Publishing, 2002
    • J. Rambau. “TOPCOM: Triangulations of Point Configurations and Oriented Matroids.” In Mathematical Software (Beijing, 2002), pages 330–340. River Edge, NJ: World Sci. Publishing, 2002. Software available at http: //www.zib.de/rambau/TOPCOM/.
    • Mathematical Software (Beijing, 2002) , pp. 330-340
    • Rambau, J.1
  • 36
    • 0001858769 scopus 로고    scopus 로고
    • Enumerative Combinatorics
    • Cambridge: Cambridge University Press
    • R. P. Stanley. Enumerative Combinatorics. Vol. 1. Cambridge Studies in Advanced Mathematics, 49. Cambridge: Cambridge University Press, 1997.
    • (1997) Cambridge Studies in Advanced Mathematics , vol.49
    • Stanley, R.P.1
  • 37
    • 0003279650 scopus 로고    scopus 로고
    • Enumerative Combinatorics
    • Cambridge: Cambridge University Press
    • R. P. Stanley. Enumerative Combinatorics. Vol. 2. Cambridge Studies in Advanced Mathematics, 62. Cambridge: Cambridge University Press, 1999.
    • (1999) Cambridge Studies in Advanced Mathematics , vol.2
    • Stanley, R.P.1
  • 38
  • 39
    • 3242727987 scopus 로고    scopus 로고
    • Computational Aspects of Root Systems, Coxeter Groups, and Weyl Characters
    • Tokyo: Math. Soc. Japan
    • J. R. Stembridge. “Computational Aspects of Root Systems, Coxeter Groups, and Weyl Characters.” In Interaction of Combinatorics and Representation Theory, MSJ Mem., 11, pp. 1–38. Tokyo: Math. Soc. Japan, 2001.
    • (2001) Interaction of Combinatorics and Representation Theory, MSJ Mem , vol.11 , pp. 1-38
    • Stembridge, J.R.1
  • 40
    • 0037609023 scopus 로고
    • On Vector Partition Functions
    • B. Sturmfels. “On Vector Partition Functions.” J. Combin. Theory Ser. A 72: 2 (1995), 302–309.
    • (1995) J. Combin. Theory Ser. A , vol.72 , Issue.2 , pp. 302-309
    • Sturmfels, B.1
  • 41
    • 33745646252 scopus 로고
    • The Littlewood– Richardson Rule—The Cornerstone for Computing Group Properties
    • Warsaw: PWN
    • B. G. Wybourne. “The Littlewood– Richardson Rule—The Cornerstone for Computing Group Properties.” In Topics in Algebra, Part 2 (Warsaw, 1988), Banach Center Publ., 26, pages 475–482. Warsaw: PWN, 1990.
    • (1990) Topics in Algebra, Part 2 (Warsaw, 1988), Banach Center Publ , vol.26 , pp. 475-482
    • Wybourne, B.G.1


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