arXiv subjects

Giovanna Carnovale

Publications and source records attributed to Giovanna Carnovale.

40 records · Page 3Linked to original sources

arXiv2003

Spherical orbits and representations of $U_ε(\mathfrak g)$

Let $U_ε(\mathfrak g)$ be the simply connected quantized enveloping algebra associated to a finite-dimensional complex simple Lie algebra $\mathfrak g$ at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of $U_ε(\mathfrak g)$ is proved for representations corresponding to the spherical conjugacy classes of the simply connected algebraic group $G$ with Lie algebra $\mathfrak g$. We achieve this result by means of a new characterization of the spherical conjugacy classes of $G$ in terms of elements of the Weyl group.

math.QA↗

arXiv2000

Some isomorphisms for the Brauer groups of a Hopf algebra

Using equivalences of categories we provide isomorphisms between the Brauer groups of different Hopf algebras. As an example, we show that when k is a field of characteristic different from 2 the Brauer groups BC(k,H_4,r_t) for every dual quasitriangular structure r_t on Sweedler's Hopf algebra H_4 are all isomorphic to the direct sum of (k,+) and the Brauer-Wall group of k. We provide an isomorphism between the Brauer group of a Hopf algebra H and the Brauer group of the dual Hopf algebra H^* generalizing a result of Tilborghs. Finally we relate the Brauer groups of H and of its opposite and co-opposite Hopf algebras.

math.RT↗

arXiv1999

On the q-convolution on the line

I continue the investigation of a q-analogue of the convolution on the line started in a joint work with Koornwinder and based on a formal definition due to Kempf and Majid. Two different ways of approximating functions by means of the convolution and convolution of delta functions are introduced. A new family of functions that forms an increasing chain of algebras depending on a parameter s>0 is constructed. The value of the parameter for which the mentioned algebras are well behaved, commutative and unital is found. In particular a privileged algebra of functions belonging to the above family is shown to be the quotient of an algebra studied in the previous article modulo the kernel of a q-analogue of the Fourier transform. This result has an analytic interpretation in terms of analytic functions whose q-moments have a particular behaviour. The same result makes it possible to extend results on invertibility of the q-Fourier transform due to Koornwinder. A few results on invertibility of functions with respect to the q-convolution are also obtained and they are related to solving certain simple linear q-difference equations with polynomial coefficients.

math.CA↗

arXiv1998

On the braided Fourier transform in the n-dimensional quantum space

We work out a theory of integrability on the braided covector Hopf algebra and braided vector Hopf algebra of type A_n as introduced by Kempf and Majid. Starting by their definition of braided Fourier transform we prove n-dimensional analogues to results by Koornwinder expressing the correspondence between products of q^2-Gaussians times monomials and products of q^2-Gaussians times q^2-Hermite polynomials under the transform. We invert the correspondence finding a suitable inverse to the transform, different from that by Kempf and Majid (our integral is not bosonic) and we show that in this case the (q-)Plancherel measure will depend on the parity of the generalized functions that we are transforming.

math.QA↗