7 papers
The Orbit Method for Finite Groups of Nilpotency Class Two of Odd Order
Aleksandrs Mihailovs
First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 wit…
Enumeration of walks on lattices. I
Aleksandrs Mihailovs
This work develops a methodical approach to counting of walks on cartesian products, biproducts, symmetric and exterior powers and bipowers, Schur operations, coverings and semicov…
Symplectic tensor invariants, wave graphs and S-tris
Aleksandrs Mihailovs
The spaces of invariants of tensor powers of the defining representation of Sp(2n) are provided with the bases parametrized by symplectic wave graphs introduced here especially for…
Diagrams of representations
Aleksandrs Mihailovs
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This a…
Fractional residues
Aleksandrs Mihailovs
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristi…
Tensor invariants of SL(n), wave graphs and L-tris
Aleksandrs Mihailovs
The space of invariants of a tensor product of representations of SL(n) is provided with the basis parametrized by wave graphs introduced here especially for this purpose. The proo…