For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite W-algebra W(g, f). We show that for the classical linear Lie algebras glN, slN, soN and spN, the operator L(z) satisfies a generalized Yangian identity. The operator L(z) is a quantum finite analogue of the operator of generalized Adler type which we recently introduced in the classical affine setup. As in the latter case, L(z) is obtained as a generalized quasideterminant.
A Lax type operator for quantum finite W-algebras / De Sole, A.; Kac, V. G.; Valeri, D.. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - 24:5(2018), pp. 4617-4657. [10.1007/s00029-018-0439-6]
A Lax type operator for quantum finite W-algebras
De Sole A.;Valeri D.
2018
Abstract
For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite W-algebra W(g, f). We show that for the classical linear Lie algebras glN, slN, soN and spN, the operator L(z) satisfies a generalized Yangian identity. The operator L(z) is a quantum finite analogue of the operator of generalized Adler type which we recently introduced in the classical affine setup. As in the latter case, L(z) is obtained as a generalized quasideterminant.File | Dimensione | Formato | |
---|---|---|---|
De Sole_A-Lax-type-operator_2018.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
864.53 kB
Formato
Adobe PDF
|
864.53 kB | Adobe PDF | Contatta l'autore |
De Sole_postprint_A-Lax-type-operator_2018.pdf
accesso aperto
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Creative commons
Dimensione
432.78 kB
Formato
Adobe PDF
|
432.78 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.