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Tilting modules for classical groups and howe duality in positive characteristics
      
We express them in terms of generatorsEij ofU(gl(n)) and as differential operators on the space of matrices These expressions are a direct generalization of the classical Capelli identities.
      
Classical invariant theory for finite reflection groups
      
We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).
      
As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
      
Applications to constructing a basis inZ(g) for classical g are also sketched.
      
This extends the results and simplifies the proof for the classical orbit structure description of [10] and [11], which applies whenF=Z.
      
A new approach to standard monomial theory for classical groups
      
As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups.
      
A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical
      
LetG be a classical algebraic group defined over an algebraically closed field.
      
The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
      
For a classical semisimple Lie algebra, we construct equivariant line bundles whose global sections afford representations with a nilpotentp-character.
      
This generalizes the classical definition of patterns in symmetric groups.
      
We prove that for classical groups the intersection C = ∩S C(S) equals D0Z where D0 = D0/K? is the universal domain in G?/K? introduced in [AG] and Z is the center of G.
      
As a corollary we prove that D0 is Stein for classical groups.
      
For this, we use a variant of classical Morse theory.
      
In this paper, we will formulate a general (parameter dependent) semistability concept for such triples, which generalizes the classical Hilbert--Mumford criterion, and we establish the existence of moduli spaces for the semistable objects.
      
Can one factor the classical adjoint of a generic matrix
      
Let k be an integral domain, n a positive integer, X a generic n × n matrix over k (i.e., the matrix (xij over a polynomial ring k[xij] in n2 indeterminates xij), and adj(X) its classical adjoint.
      
 

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