V.G. Kac and M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, Lie Theory and Geometry: In Honor of Bertram Kostant, J.-L. Brylinski ed., Birkhauser Prog. in Math. 123, Boston 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Tensor Product Representations for Orthosymplectic Lie.. - Benkart, Shader, Ram (Correct)
....of the use of tableaux in the study of representations of Lie superalgebras. f) There is an extensive literature of papers by Bernstein and Leites [BL] Le1 Le2] Kac [K1 K2] van der Jeugt, Hughes, King, and Thierry Mieg [JHKT1 JHKT3] Penkov and Serganova [PS1 PS3] P] Kac and Wakimoto [KW], and others which studies representations of Lie superalgebras using Lie theoretic and geometric methods. These approaches also yield character formulas, the most general of which is the Weyl Kac character formula. We have not made any effort to understand our character formulas in this other ....
V.G. Kac and M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, Lie Theory and Geometry: In Honor of Bertram Kostant, J.-L. Brylinski ed., Birkhauser Prog. in Math. 123, Boston 1994.
THE RAMANUJAN JOURNAL, 5, 111--128, 2001 c - Appell's Function And (Correct)
....on elliptic curves. This function was introduced by M. P. Appell in [2] in order to decompose into simple elements the so called elliptic functions of the third kind (which correspond to meromorphic sections of line bundles on elliptic curves) 1 In the recent paper of V. G. Kac and M. Wakimoto [6] the function # appeared in connection with characters of affine Lie superalgebras. As is well known Riemann s theta function arises naturally when considering global sections of line bundles on elliptic curves. We claim that the function # is connected in a similar way with rank 2 bundles. ....
V.G. Kac and M. Wakimoto, "Integrable Highest Weight Modules Over Affine Super-Algebras and Appell's Function," prepring math-ph/0006007.
Fragments by Ramanujan on Lambert Series - Berndt (Correct)
....formula for the number of ways an integer can be represented as a sum of six triangular numbers. Although we expect that this formula is in the classical literature, we have been unable to find it there. The only appearances of this formula known to us appear in papers of V. G. Kac and M. Wakimoto [14] in 1994 and K. Ono, S. Robins, and P. T. Wahl [20] in 1995. Let r k (n) denote the number of ways the positive integer n can be represented as a sum of k squares, with representations arising from different signs and from different orders being regarded as distinct. By convention, r k (0) 1: ....
....have discovered formulas for r 2k (n) for certain values of k: For very comprehensive lists of references to the classical literature on r 2k (n) see the papers [18] 19] by S. C. Milne in which he develops general methods for deriving infinite families of formulas for r 2k (n) Kac and Wakimoto [14] have also found infinite families of formulas for r 2k (n) FRAGMENTS BY RAMANUJAN ON LAMBERT SERIES 3 Entry 4 (formula (3.21) p. 356) 2 (q 4 ) 1 X n=0 ( Gamma1) n q 2n 1 Gamma q 4n 2 : We have replaced q by q 4 in Ramanujan s formulation. It is easy to show that Entry 4 ....
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V. G. Kac and M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, Lie Theory and Geometry (J.--L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds.), Birkhauser, Boston, 1994.
The Remaining 40% Of Ramanujan's Lost Notebook - Berndt (Correct)
.... 1) 2 q (2n 1) 2 1 Gamma q 2n 1 gives the corollary t 6 (n) 1 8 X dj(4n 3) dj3 (mod 4) d 2 Gamma 1 8 X dj(4n 3) dj1 (mod 4) d 2 : We have been unable to find this formula in the classical literature. The first occurrences known to us are in recent papers by Kac and Wakimoto [9] and by Ono, Robins, and Wahl [12] We have found a proof along the lines of Ramanujan s thinking. Incomplete Elliptic Integrals of the First Kind Some of the most amazing formulas in the lost notebook involve incomplete elliptic integrals. We cite just one of several examples. Recall that ....
V. G. Kac and M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, Lie Theory and Geometry (J.--L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds.), Birkhauser, Boston, 1994. BRUCE C. BERNDT
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