Related papers: Quantum SL(3,C)'s: the missing case
We study and classify almost all quantum SL(3,C)'s whose representation theory is ``similar'' to that of the (ordinary) group SL(3,C). Only one case, related to smooth elliptic curves, could not be treated completely.
We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.
The q-field theories are constructed by substituting quantum groups for the usual Lie groups. In earlier papers this construction was carried out for the quantum group SU_q(2). Here the investigation is extended to SL_q(3). The resulting…
SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the…
The article has been withdrawn by the author.
It has recently been suggested that an exactly solvable problem characterized by a new quantum number may underlie the electronic shell structure observed in the mass spectra of medium-sized sodium clusters. We investigate whether the…
We continue our study of minimal affinizations for algebras of type D, E.
The article is taken out.
We present a partial classification of those finite linear spaces $\mathcal{S}$ on which an almost simple group $G$ with socle $PSL(3,q)$ acts line-transitively.
This paper consists of $3$ parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second part, the notion of quantum hidden process is introduced. In…
We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).
In this paper the detailed classification of three-dimensional exceptional canonical hypersurface singularities which don't satisfy the condition of well-formedness is given. This result completes the classification of three-dimensional…
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence…
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The…
We present the subalgebra structure of sl(3,O), a particular real form of e6 chosen for its relevance to particle physics and its close relation to generalized Lorentz groups. We use an explicit representation of the Lie group SL(3,O) to…
We categorify the idempotented form of quantum sl(n).
We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.We survey some of our old results given in [CE95] and [CE10] and present some new ones in the last three sections.
We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…
In this paper we classify the orbits of the group SL(3,F)^3 on the space F^3\otimes F^3\otimes F^3 for F=C and F=R. This is known as the classification of complex and real 3-qutrit states. We also give an overview of physical theories where…