Some of my research is reflected on my webpage. Namely,
I am the author and a coauthor of many sequences in the OEIS. I have a separate web page with the list of my sequences.
Number Gossip. Combinatorics arXiv 0804.2277.
Autobiographical Numbers. Combinatorics arXiv 0803.0270.
9 Divides no Odd Fibonacci. Combinatorics arXiv 0712.3509.
I discuss numbers that divide no odd Fibonacci. The number 9 plays a special role among such numbers.
How to Create a New Integer Sequence. Combinatorics arXiv 0712.2244.
I discuss standard procedures used to create new sequences from a given sequence or from a given pair of sequences.
Unique Tournaments and Radar Tracking. Combinatorics arXiv 0712.1621.
I build a bijection between unique tournaments and binary strings representing no track for a specific radar tracking rule.
(with M. Curry and M. Flint) Decentralized Control Using Global Optimization (DCGO). AIAA Infotech@Aerospace 2007 Conference Proceedings (2007).
Global-scope plans for the team are generated and distributed using the principle of emergent leadership to provide efficient plan generation and execution with minimal performance degradation compared to a centralized controller under delayed communications.
(with Ingrid Daubechies and Konstantinos Drakakis) A Detailed Study of the Attachment Strategies of New Autonomous Systems in the AS Connectivity Graph. Internet Mathematics, v.2, n2, 185-246 (2005).
In the first part of this paper, we use real BGP data to study some properties of the AS connectivity graph and its evolution in time. In the second part, we build a simple model that is inspired by observations made in the first part, and we discuss simulations of this model.
(with J. Bernstein) Quantum groups and representations with highest weight. Quantum Algebra and Topology arXiv q-alg/9704007.
We connect quantum groups to minimal objects in the category of representations with highest weight λ: they correspond to irreducible representations.
On quantum group GLp,q(2). Quantum Algebra and Topology arXiv q-alg/9701033.
In the Hopf algebra GLp,q(2) the determinant is central iff p=q. In this case we put determinant to be equal to 1 to get SLq(2). In this paper I consider the case when p/q is a root of unity; and, consequently, a power of the determinant is central.
(with J.Bernstein) On Quantum Group SLq(2). Comm. Math. Phys., v.117, n3, 691-708 (1996).
We show how to construct the quantum group SLq(2), starting from the Hopf algebra of regular functions on the torus, adding some natural conditions. Our approach allows us to construct metaplectic quantum groups of the SL(2)-type.
Tetramodules over Hopf Algebra of Regular Functions on a Torus. IMRN, No.7, 275-284 (1994).
Discussion of the definition of "tetramodule," (a special kind of bimodule and bicomodule), its properties, and its applications.
Sturm-Liouville Operators Connected with Superanalogs of Virasoro algebra. Reports of Department of Mathematics, University of Stockholm, Sweden, 1988, No.5, 67-76.
We describe different ways of superizing the Sturm-Liouville operator.
(with O. Ovsienko) Superversion of Miura Transformations. Reports of Department of Mathematics, University of Stockholm, Sweden, 1988, No.5, 60-66.
The Miura transformation of the Korteveg-de Vries equation can be described in terms of the Virasoro algebra. We construct the analog of the Miura transformation for the Lie superalgebras of the Neveu-Schwarz type.
The Korteweg-de Vries Superequation Related to the Lie Superalgebra of Neveu-Schwarz-2 String Theory. Teor. Mat. Fiz., 72, No.2, 899-904 (1987).
The short version of the next paper.
Superization of the Korteveg-de Vries Equation Related with the Neveu-Schwarz Superalgebra NS(2). Reports of Department of Mathematics, University of Stockholm, Sweden, 1986, No.21, 58-73.
We construct the integrable Korteveg-de Vries type super-equation related to the Neveu-Schwarz superalgebra NS(2) by means of the hamiltonian reduction method from the Kac-Moody algebra $\widehat {sl(2,1)}$.
Lie Superalgebra Structure on Eigenfunctions and Jets of Resolvent's Kernel, near the Diagonal of an n-th Order Ordinary Differential Operator. in 'Integrable and Superintegrable Systems' ed. B.A.Kupershmidt. World Scientific 1990, p.321-335.
An n-th order ordinary differential operator can be regarded as a point in the dual space of the Lie superalgebra $\widehat {gl(n,1)}$. The stabilizer of this point in the coadjoint action inherits the structure of the Lie superalgebra and can be described as the direct sum of the jets of the kernel of the resolvent of, and the eigenfunctions of, the given differential operator.
Structure of Lie Superalgebras on Eigenfunctions and Jets of the Kernel of the Resolvent near the Diagonal for an n-th-order Differential Operator. Funkts. Anal. Prilozhen., 20, No.2, 162-164 (1986).
The short version of the previous one.
Lie Superalgebra osp(1,2), Neveu-Schwarz Superalgebra and Superization of Korteweg-de Vries equation. Group Theoretical Methods in Physics. Proceedings of the third seminar: Yurmala 1985. Utreht, Netherlands, VNU Science Press, 1986, v.1, 307-315.
The description of the super Korteveg-de Vries equation and the Neveu-Schwarz superalgebra as the Hamiltonian reduction of the Lie superalgebra $\widetilde{osp(1,2)}$.
The Gel'fand-Dikii Algebras and the Virasoro Algebra. Funkts. Anal. Prilozhen. 20, No.4, 332-334 (1986).
An investigation of the Gelfand-Dikii algebras as the generalizations the of Virasoro algebra.
Representation Models and Generalized Clifford Algebras. Funkts. Anal. Prilozhen., 16, No.4, 322-323 (1982).
For every simply-laced Dynkin diagram Δ of a Lie algebra G, we construct a generalization of the Clifford algebra, CΔ. The involutive subalgebra of G can be imbedded into CΔ. Using the induced representation of the involutive subalgebra in CΔ we construct the model representation of G - the direct sum of irreducible representations taken once each.
Send mail to: Tanya Khovanova
tanyakh@yahoo.comRevised August 2008