The Galois group of a Schubert problem is a subtle invariant that encodes intrinsic structure of its set of solutions. These geometric invariants are difficult to determine in general. However, based on a special position argument due to Schubert and a combinatorial criterion due to Vakil, we show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. The result follows from a particular inequality of Schubert intersection numbers which are Kostka numbers of two-rowed tableaux. In most cases, the inequality follows from a combinatorial injection. For the remaining cases, we use that these Kostka numbers appear in the tensor product decomposition of sl2C-modules. Interpreting the tensor product as the action of certain Toeplitz matrices and using spectral analysis, the inequality can be rewritten as an integral. We establish the inequality by estimating this integral using only elementary Calculus.

Schubert calculus has become an indispensable tool for enumerative geometry. It concerns the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The polynomials that represent the Schubert classes are called Schubert polynomials. An ongoing project in Schubert calculus has been to provide geometric foundations for the combinatorics. An example is the recovery by Knutson and Miller of the Schubert polynomials for finite flag varieties as the equivariant cohomology classes of matrix Schubert varieties. The present thesis is the start of a project to recover Schubert polynomials for the Borel-Moore homology of the (special linear) affine Grassmannian by an analogous process. This requires finitizing an affine Schubert variety to produce a matrix affine Schubert variety. This involves a choice of ``window'', so one must then identify a class representative that is independent of this choice. Examples lead us to conjecture that this representative is a k-Schur function. Concluding the discussion is a preliminary investigation into the combinatorics of Gröbner degenerations of matrix affine Schubert varieties, which should lead to a combinatorial proof of the conjecture. / Ph. D.

No description available.

The arpeggione is an instrument invented and built in1823 by the Viennese instrument maker Johann Georg Staufer. This instrument has the shape of guitar but bowed like a cello, thus it¡¦s called the ¡§guitar violoncello¡¨. During its short life lasted for no more than a decade, we are fortunate there survived an ¡§Arpeggione Sonata, D821¡¨ composed by Franz Schubert in 1824. This thesis discusses on the style of this composition and the historical background of arpeggione, with more focus on the interpretation and technique in the arrangement for cello. After arpeggione had vanished from the musical scene, several arrangements for different instruments of this work had published. The Spanish cellist Gasper Cassadó even expanded this work as a cello concerto, which is more suitable for cello playing. From these aspects, we can build up a more insight into this charming piece.

Thesis. / Includes bibliographical references.

Thesis (Ed. D.)--Teachers College, Columbia University. / Typescript; issued also on microfilm. Sponsor: Frederick D. Mayer. Dissertation Committee: Charles W. Walton, Craig A. Timberlake. Includes bibliographical references.

Diss.--Münster, 1991. / Bibliogr. p. 239-251. Index.

Thesis. / Includes bibliographical references.

Inaug.-Diss.-Bonn. / Vita. Bibliography: p. 285-289.

Thesis (M.A.)--University of Wisconsin--Madison, 1941. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 87-90).