%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Aleksandrs Mihailovs",
%%%     date            = "January 16, 2000",
%%%     filename        = "MihailovsA.bib",
%%%     url             = "http://www.mihailovs.com/Alec/MihailovsA.bib",
%%%     www-home        = "http://www.mihailovs.com/Alec/",
%%%     address         = "Department of Mathematics,
%%%                        Shepherd College,
%%%                        Shepherdstown, WV 25401, USA",
%%%     telephone       = "+1 304 262 8760",
%%%     FAX             = "+1 304 262 8760",
%%%     email           = "Alec at Mihailovs.com",
%%%     dates           = {1955--},
%%%     keywords        = "representation theory, combinatorics, number theory",
%%%     supported       = "yes",
%%%     supported-by    = "Aleksandrs Mihailovs",
%%%     abstract        = "Bibliography for Aleksandrs Mihailovs"
%%%  }
%%% ====================================================================

@misc{MihailovsA:orb,
        author    = {Aleksandrs Mihailovs},
        title     = {The Orbit Method for Finite Groups of Nilpotency Class Two of Odd Order}, 
	eprint 	  = {math.RT/0001092},
        pages     = 16,
        year      = 2000,
	url	  = {http://www.mihailovs.com/Alec/orb.dvi},
	abstract  = {First, I construct an isomorphism between the categories of
		    (topological) groups of nipotency class 2 with 2-divisible center and
		    (topological) Lie rings of nipotency class 2 with 2-divisible center. 
		    That isomorphism allows us to construct adjoint and coadjoint
		    representations as usual. For a finite group G of nipotency class 2 
		    of odd order, I construct a basis in its group algebra C[G],
		    parameterized by elements of g* so that the elements of 
		    coadjoint orbits form bases of simple two-side ideals of C[G]. 
		    That construction gives us a one-to-one correspondence between 
		    G-orbits in g* and classes of equivalence of irreducible unitary 
		    representations of G, implying a very simple character formula. 
		    The properties of that correspondence are similar to the 
		    properties of the analogous correspondence given by Kirillov's 
		    orbit method for nilpotent connected and simply connected Lie 
		    groups. The diagram method introduced in my thesis, gives us a 
		    convenient way to study normal forms on the orbits and 
		    corresponding representations. }}

@phdthesis{MihailovsA:phd,
        author    = {Aleksandrs Mihailovs},
        title     = {A Combinatorial Approach to Representations of {L}ie Groups and Algebras},
        school    = {University of Pennsylvania},
        year      = 1998,
	url	  = {http://www.mihailovs.com/Alec/thesis.dvi}, 
	abstract  = {First I describe 
		    the invariants and decompositions of tensor products of polynomial representations of 
		    SL(2) in the terms of outerplanar graphs, i.e. graphs with the vertices 0, 1, ..., m,  
		    the edges of which can be drawn in the upper half-plane without intersections. Then I use 
		    wave graphs introduced here to give an analogous description for tensor invariants 
		    of SL(n) and Sp(2n).
		    I use quite a different combinatorial approach to the description of the representations of 
   		    unipotent groups of Lie type, through 'diagrams of representations'. This approach leads 
		    to various applications, including explicit formulas for fractional residues 
		    (i.e. invariants of some generalizations of differential forms). 
		    Conversely, these combinatorial approaches to representations allow us 
		    to use known representation-theoretical results to get the explicit formulas for the 
		    enumeration of the corresponding combinatorial objects, 
		    like walks on lattices, or the counting of some specific graphs.}}

@misc{MihailovsA:walks,
        author    = {Aleksandrs Mihailovs},
        title     = {Enumeration of Walks on Lattices. {I}}, 
	eprint 	  = {math.CO/9803128},
        pages     = 37,
        year      = 1998,
	url	  = {http://www.mihailovs.com/Alec/walks.dvi},
	abstract  = {This work develops a methodical approach to counting of 
		     walks on cartesian products, biproducts, symmetric and exterior 
		     powers and bipowers, Schur operations, coverings and semicoverings 
		     of weighted graphs. For weight and root lattices of semisimple 
		     Lie algebras, this approach allows us to compute various combinatorial 
		     and representation-theoretical constants, in particular, the number of 
		     plane symplectic wave graphs with given number of vertices.}}

@misc{MihailovsA:spn,
        author    = {Aleksandrs Mihailovs},
        title     = {Symplectic Tensor Invariants, Wave Graphs and {S}-tris}, 
	eprint    = {math.RT/9803102}, 
        pages     = 16,
        year      = 1998,
	url	  = {http://www.mihailovs.com/Alec/spn.dvi},
	abstract  = {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 this purpose. The proof utilizes a game similar 
		     to Tetris,  named here S-tris. This work continues my previous work  
		     on the tensor invariants of SL(n), wave graphs and L-tris.}}

@misc{MihailovsA:diag,
        author    = {Aleksandrs Mihailovs},
        title     = {Diagrams of Representations}, 
	eprint    = {math.RT/9803079}, 
        pages     = 19,
        year      = 1998,
	url	  = {http://www.mihailovs.com/Alec/diag.dvi},
	abstract  = {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 article explains how to use 
		     these diagrams to describe normal forms, orbits and invariants of 
		     the representation, especially for the case of nilpotent Lie algebras.}}

@misc{MihailovsA:frac,
        author    = {Aleksandrs Mihailovs},
        title     = {Fractional Residues}, 
	eprint 	  = {math.RT/9803018}, 
        pages     = 17,
        year      = 1998,
	url	  = {http://www.mihailovs.com/Alec/frac.dvi},
	abstract  = {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 characteristic, 
		     a new invariant of formal power series, a width, is defined. 
		     Some applications to the geometric quantization of a line and 
		     conformal quantum field theory are discussed as well.}}

@misc{MihailovsA:sln,
        author    = {Aleksandrs Mihailovs},
        title     = {Tensor Invariants of {SL}(n), Wave Graphs and {L}-tris}, 
	eprint    = {math.RT/9802119}, 
        pages     = 8,
        year      = 1998,
        url       = {http://www.mihailovs.com/Alec/sln.dvi},
        abstract  = {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 proof utilizes a game similar to Tetris,  
                     named here L-tris.}} 

@unpublished{MihailovsA:brief,
        author    = {Aleksandrs Mihailovs},
        title     = {A Brief Outline of My Current and Intended Research},
        pages     = 2,
        year      = 1997,
        url       = {http://www.mihailovs.com/Alec/brief.dvi}}

@misc{MihailovsA:sl2ten,
        author    = {Aleksandrs Mihailovs},
        title     = {Tensor Decompositions for {SL}(2) and Outerplanar Graphs},
	eprint    = {math.RT/9712259}, 
        pages     = 21, 
        year      = 1997,
        note      = {Accepted for publication by Journal of Combinatorial Theory, Series A},
        url       = {http://www.mihailovs.com/Alec/sl2ten.dvi},
        abstract  = {The main result of this article is the decomposition of tensor products 
                     of representations of SL(2) in the sum of irreducible representations 
                     parametrized by outerplanar graphs. 
                     An outerplanar graph is a graph with the vertices 0, 1, 2, ..., m, 
                     edges of which can be drawn in the upper half-plane without intersections. 
                     I allow for a graph to have multiple edges, but don't allow loops.}} 

@unpublished{MihailovsA:sl2,
        author    = {Aleksandrs Mihailovs},
        title     = {Tensor Invariants of {SL}(2) and Outerplanar Graphs},
        pages     = 7,
        year      = 1997,
        url       = {http://www.mihailovs.com/Alec/sl2.dvi},
        abstract  = {The space of invariants of a tensor product of representations of SL(2)
                     is provided with the basis parametrized by outerplanar graphs.}} 

@unpublished{MihailovsA:weights,
        author    = {Aleksandrs Mihailovs},
        title     = {Weights and Roots},
        pages     = 5,
        year      = 1997,
        url       = {http://www.mihailovs.com/Alec/weights.dvi},
        abstract  = {A survey of the basic constructions used to classify and study 
                     representations and invariants of semisimple Lie groups and algebras.}} 

@mastersthesis{MihailovsA:master,
        author  = {Aleksandrs Mihailovs},
        title   = {The {P}etrovsky numbers and multiplicities of representations},
        school  = {University of Latvia},
        year    = 1995}

@unpublished{MihailovsA:bachelor,
        author    = {Aleksandrs Mihailovs},
        title     = {Lucky tickets and the {P}etrovsky numbers},
        year      = 1995,
        note      = {Bachelor's thesis, University of Latvia}}
        
@article{MihailovsA:logcon,
        author   = {Aleksandrs Mihailovs},
        title    = {On the Log-concavity},
        journal  = {Kvant},
        number   = {11/12},
        year     = 1993,
        pages    = {1--9}}