 
Summary: Quantized coinvariants at transcendental q
K R Goodearl and T H Lenagan #
Abstract
A general method is developed for deriving Quantum First and Second Funda
mental Theorems of Coinvariant Theory from classical analogs in Invariant Theory,
in the case that the quantization parameter q is transcendental over a base field. Sev
eral examples are given illustrating the utility of the method; these recover earlier
results of various researchers including Domokos, Fioresi, Hacon, Rigal, Strickland,
and the present authors.
2000 Mathematics Subject Classification: 16W35, 16W30, 20G42, 17B37, 81R50.
Keywords: coinvariants, First Fundamental Theorem, Second Fundamental Theorem,
quantum group, quantized coordinate ring.
Introduction and background
In the classic terminology of Hermann Weyl [18], a full solution to any invariant theory
problem should incorporate a First Fundamental Theorem, giving a set of generators (fi
nite, where possible) for the ring of invariants, and a Second Fundamental Theorem, giving
generators for the ideal of relations among the generators of the ring of invariants. Many
of the classical settings of Invariant Theory have quantized analogs, and one seeks corre
sponding analogs of the classical First and Second Fundamental Theorems. However, the
setting must be dualized before potential quantized analogs can be framed, since there
