We give a purely combinatorial proof of the positivity of the stabilized forms of the
generalized exponents associated to each classical root system. In finite type, we rederive …

We give a new combinatorial interpretation of Howe dual pairs of the form (g, Sp 2 ℓ), where
g is a Lie (super) algebra of classical type. This is done by establishing a symplectic …

We give a new formula for the branching rule from GL n to O n generalizing the Littlewood's
restriction formula. The formula is given in terms of Littlewood-Richardson tableaux with …

The Newell-Littlewood numbers are defined in terms of their celebrated cousins, the
Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical …

Consider the symmetric pair $(\textbf {GL} _n,\textbf {O} _n) $ in the setting of the Kostant-
Rallis Theorem. We provide a combinatorial formula for the graded multiplicity of an …

We prove Macdonald-type deformations of a number of well-known classical branching
rules by employing identities for elliptic hypergeometric integrals and series. We also …

In the first part of this thesis, we make use of representation theory of groups and algebras to
perform an irreducible decomposition of tensors in the context of metric-affine gravity. In …

We describe how traceless projection of tensors of a given rank can be constructed in a
closed form. On the way to this goal we invoke the representation theory of the Brauer …

We study iterated Pieri rules for representations of classical groups. That is, we consider
tensor products of a general representation with multiple factors of representations …

We provide an explicit combinatorial description of the embedding of the crystal of
Kashiwara–Nakashima tableaux in types B and C into that of i-Lusztig data associated to a …