Communications in Mathematical Physics

, Volume 136, Issue 3, pp 543–566 | Cite as

Combinatorics of representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) atq=0

  • Michio Jimbo
  • Kailash C. Misra
  • Tetsuji Miwa
  • Masato Okado


Theq=0 combinatorics for\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) is studied in connection with solvable lattice models. Crystal bases of highest weight representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) approximate the crystal graphs of levell representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\). The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\).


Tensor Product High Weight Weight Vector Transfer Matrix Symmetric Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Michio Jimbo
    • 1
  • Kailash C. Misra
    • 2
  • Tetsuji Miwa
    • 3
  • Masato Okado
    • 4
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  4. 4.Department of Mathematical Science, Faculty of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan

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