RT Journal Article T1 A new family of N-fold supersymmetry: type B A1 González López, Artemio A1 Tanaka, Toshiaki AB We construct a new family of N -fold supersymmetric systems which is referred to as “type B”. A higher-derivativerepresentation of the N -fold supercharge for this new family is given by a deformation of the type A N -fold supercharge.By utilizing the same method as in the sl(2) construction of type A N -fold supersymmetry, we show that this family includestwo of the quasi-solvable models of Post–Turbiner type PB Elsevier Science BV SN 0370-2693 YR 2004 FD 2004-04-22 LK https://hdl.handle.net/20.500.14352/51550 UL https://hdl.handle.net/20.500.14352/51550 LA eng NO [1] A.V. Turbiner, A.G. Ushveridze, Phys. Lett. A 126 (1987) 181. [2] M.A. Shifman, Int. J. Mod. Phys. A 4 (1989) 2897. [3] A.G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics, IOP, Bristol, 1994. [4] A. González-López, N. Kamran, P.J. Olver, Contemp. Math. 160 (1994) 113. [5] A.A. Andrianov, M.V. Ioffe, V.P. Spiridonov, Phys. Lett. A 174 (1993) 273. [6] E. Witten, Nucl. Phys. B 188 (1981) 513. [7] E. Witten, Nucl. Phys. B 202 (1982) 253. [8] A.A. Andrianov, M.V. Ioffe, F. Cannata, J.-P. Dedonder, Int. J. Mod. Phys. A 10 (1995) 2683. [9] A.A. Andrianov, M.V. Ioffe, D.N. Nishnianidze, Phys. Lett. A 201 (1995) 103. [10] A.A. Andrianov, M.V. Ioffe, D.N. Nishnianidze, Theor. Math. Phys. 104 (1995) 1129. [11] V.G. Bagrov, B.F. Samsonov, Theor. Math. Phys. 104 (1995) 1051. [12] B.F. Samsonov, Mod. Phys. Lett. A 11 (1996) 1563. [13] V.G. Bagrov, B.F. Samsonov, Phys. Part. Nucl. 28 (1997) 374. [14] B.F. Samsonov, Phys. Lett. A 263 (1999) 274. [15] D.J. Fernández C., Int. J. Mod. Phys. A 12 (1997) 171. [16] J.O. Rosas-Ortiz, J. Phys. A 31 (1998) 10163. [17] B. Bagchi, A. Ganguly, D. Bhaumik, A. Mitra, Mod. Phys. Lett. A 14 (1999) 27. [18] D.J. Fernández C., V. Hussin, J. Phys. A 32 (1999) 3603. [19] D.J. Fernández C., J. Negro, L.M. Nieto, Phys. Lett. A 275 (2000) 338. [20] M. Plyushchay, Int. J. Mod. Phys. A 15 (2000) 3679. [21] S. Klishevich, M. Plyushchay, Mod. Phys. Lett. A 14 (1999) 2739. [22] H. Aoyama, H. Kikuchi, I. Okouchi, M. Sato, S. Wada, Nucl. Phys. B 553 (1999) 644. [23] H. Aoyama, M. Sato, T. Tanaka, M. Yamamoto, Phys. Lett. B 498 (2001) 117. [24] S.M. Klishevich, M.S. Plyushchay, Nucl. Phys. B 606 (2001) 583. [25] S.M. Klishevich, M.S. Plyushchay, Nucl. Phys. B 616 (2001) 403. [26] P. Dorey, C. Dunning, R. Tateo, J. Phys. A 34 (2001) 5679. [27] P. Dorey, C. Dunning, R. Tateo, J. Phys. A 34 (2001) L391. [28] H. Aoyama, M. Sato, T. Tanaka, Nucl. Phys. B 619 (2001) 105. [29] H. Aoyama, M. Sato, T. Tanaka, Phys. Lett. B 503 (2001) 423. [30] H. Aoyama, N. Nakayama, M. Sato, T. Tanaka, Phys. Lett. B 519 (2001) 260. [31] T. Tanaka, Nucl. Phys. B 662 (2003) 413. [32] A.V. Turbiner, Commun. Math. Phys. 118 (1988) 467. [33] A. González-López, N. Kamran, P.J. Olver, Commun. Math. Phys. 153 (1993) 117. [34] R. Sasaki, K. Takasaki, J. Phys. A 34 (2001) 9533. [35] M. Sato, T. Tanaka, J. Math. Phys. 43 (2002) 3484. [36] F. Cannata, M.V. Ioffe, D.N. Nishnianidze, J. Phys. A 35 (2002) 1389. [37] A.A. Andrianov, A.V. Sokolov, Nucl. Phys. B 660 (2003) 25. [38] G. Post, A. Turbiner, Russ. J. Math. Phys. 3 (1995) 113. [39] T. Tanaka, Ann. Phys. 309 (2004) 239, hep- th/0306174. [40] A. González-López, T. Tanaka, in preparation. NO ©2004 Elsevier B.V..This work was partially supported by the DGI under grant No. BFM2002-02646 (A.G.-L.) and by a JSPS research fellowship (T.T.). One of us (T.T.) would like to thank A.A. Andrianov and M. Sato for useful discussions, as well as all the members of the Departamento de Física Teórica II, Universidad Complutense, for their kind hospitality during his stay. NO DGI, Spain NO JSPS (TT) DS Docta Complutense RD 30 abr 2024