Polynomial relations in the center of U-q(sl(N))

Arnaudon, Daniel; Bauer, Michel

doi:10.1007/BF00805857

Polynomial relations in the center of U-q(sl(N))

Daniel Arnaudon
(
- CERN and
- Annecy, LAPP
)
,
Michel Bauer
(
- CERN
)

Oct, 1993

6 pages

Published in:

Lett.Math.Phys. 30 (1994) 251

e-Print:

hep-th/9310030 [hep-th]

DOI:

10.1007/BF00805857

Report number:

CERN-TH-7025-93,
ENSLAPP-A-437-93

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Abstract: (desy)

When the parameter of deformation

q

is a root of unity, the centre of

{\cal U}_q(sl(N))

contains, besides the usual

q

-deformed Casimirs, a set of new generators which are basically the

m

-th powers of all the Cartan generators of

{\cal U}_q(sl(N))

. All these central elements are however not independent. In this letter, generalising the well-known case of

{\cal U}_q(sl(2))

, we write explicitely polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.

References(4)

Figures(0)

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