Field of U-invariants of adjoint representation of the group GL(n,K)
We obtain system of generators of the field of U-invariants of ajoint representation of the group GL(n,K).
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arXiv subjects
A. N. Panov
Publications and source records attributed to A. N. Panov.
Regular N-orbits in the nilradical of a parabolic subalgebra
In the present paper the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra is studied. We set up general conjectures on the construction of the field of invariants and the structure of orbits of maximal dimension. The conjecture is proved for parabolic subalgebras of special types.
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Representations of solvable Lie algebras with filtrations
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
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Tangent Cones of Schubert Varieties for $A_n$ of lower rank
We calculate the tangent cones at unity of Schubert varieties for $A_n$, where $n$ is less or equal to four. We state several conjectures for an arbitrary $n$.
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Representations of quantum orders
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted polynomials, the quantum Weyl algebra and the algebra of regular functions on quantum group.
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Reduction of spherical functions
Using reduction of spherical functions, we obtain generators of the algebra and the field of invariants for the coadjoint representation of Borel and maximal nilpotent subalgebras of simple Lie algebras.
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Invariants of coadjoint representation of regular factors
A regular factor is a factor algebra of the unitriangular Lie algebra with respect to some regular ideal. In the paper we construct system of generators of the field of invariants for the coadjoint representation of an arbitrary regular factor.
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Diagram method in research on coadjoint orbits
We correspond to any factor algebra of the unitriangular Lie algebra with respect to a regular ideal some permutation. In terms of this permutation one can construct a diagram, that allows to calculate index and maximal dimension of coadjoint representation.
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Coadjoint orbits of the group $UT(7,K)$
We present the classification of coadjoint orbits of the unitriangular group $UT(7, K)$. We also describe subregular orbits of $UT(n, K)$ for an arbitrary $n$.
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Involutions in $S_n$ and associated coadjoint orbits
In the paper we study the coadjoint orbits of the group $\mathrm{UT}(n,K)$ associated with involutions. We obtain a formula for dimension of the orbit. We construct a polarization for the canonical element of orbit. We find a system of generators in the defining ideal of orbit.
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On index of certain nilpotent Lie algebras
We introduce the method of calculation of index of Lie algebras that are factors of the unitriangular Lie algebra with respect to ideals spanned by subsets of root vectors.
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Irreducible representations of quantum solvable algebras at roots of 1
We study the irreducible representations of quantum solvable algebras at roots of 1 which lie over a point of the variety of center. We characterize the quiver of fiber algebra and present the formulas on the dimension and the number of these representations in terms of Poisson structure of the variety of center.
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Quantum solvable algebras. Ideals and representations at roots of 1
There studed correspondence between symplectic leaves, irreducible representations and prime ideals, which is invariant with respect to quantum adjoint action. The Conjecture of De Concini-Kac-Procesi on dimensions of irreducible representations is proved for sufficiently great $l$.
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Stratification of prime spectrum of quantum solvable algebras
A quantum solvable algebra is an iterated $q$-skew extension of a commutative algebra. We get finite statification of prime spectrum for quantum solvable algebras obeying some natural conditions. We prove that for any prime ideal $I$ the skew field of fractions $Fract(R/I)$ is isomorphic to the skew field of fractions of an algebra of twisted polynomials (Quantum Gel'fand-Kirillov Conjecture).
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Fields of fractions of quantum solvable algebras
We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted rational functions. This is the quantum version of Gelfand-Kirillov conjecture for solvable algebraic Lie algebras.
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