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Monday, May 4, 2020 | History

2 edition of Integral forms for Weyl modules of GL(2,Q) found in the catalog.

Integral forms for Weyl modules of GL(2,Q)

Perdita Emma Stevens

# Integral forms for Weyl modules of GL(2,Q)

## by Perdita Emma Stevens

• 54 Want to read
• 6 Currently reading

Written in English

Edition Notes

Thesis (Ph.D.) - University of Warwick, 1992.

 ID Numbers Statement Perdita Emma Stevens. Open Library OL19430193M

6 Rankin-Selberg L-function for GL(3) × GL(2) over totally real ﬁelds F,in which case our period relation is new. Combined with the Gelbart-Jacquet lift, Theorem A therefore implies the analogous rationality result for triple products of Hilbert modular forms f⊗f⊗gin the balanced case (we refer to [13, 14] for. Analysis on Lie Groups An Introduction book form. Topics covered include the Haar measure and invariant integration, 99 D. Goldfeld Automorphic Forms and L-Functions for the Group GL(n,R) M. Marcus & J. Rosen Markov Processes, Gaussian Processes, and Local Times.

We will have a gentle introduction to the theory of modular forms and functions. Then, we shall give some examples of their applications in number theory, in particular, to theory of integer lattices. Examples may include 1) counting lattice points on a sphere, 2) finding all even integral self-dual lattices in 24 dimensional Euclidean space.   § Z-forms of U[sub(v)](gl[sub(n)]) § Integral quantum Schur–Weyl reciprocity § A connection with Ringel–Hall algebras ; Exercises and notes ; Appendices ; Appendix A. Varieties and affine algebraic groups §A Affine varieties §A Varieties §A Affine.

modules for such algebras, including the character formula of Hermann Weyl. It. concludes with the theory of Chevalley orders. Chapter 9 is devoted to the. theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. . Measure, Integral and Probability, Second Edition M. Capi´nksi and E. Kopp Multivariate Calculus and Geometry, Second Edition S. Dineen Numerical Methods for Partial Differential Equations G. Evans, J. Blackledge, P. Yardley Probability Models Real Analysis J.M. Howie Sets, Logic and Categories P. Cameron Special Relativity N.M.J File Size: 3MB.

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### Integral forms for Weyl modules of GL(2,Q) by Perdita Emma Stevens Download PDF EPUB FB2

We will construct the Lusztig form for the quantum loop algebra of $\mathfrak{gl}_n$ by proving the conjecture \cite[]{DDF} and establish partially the Schur--Weyl duality at the integral. A Note on Weyl Modules for ∞ and ∞ The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations.

The second is the. and the integral Schur–Weyl duality for types other than A. This book takes an algebraic approach to the aﬃne quantum Schur–Weyl theory. The book begins with a study of extended Ringel–Hall algebras associated with the cyclic quiver of n vertices and the Green–Xiao Hopf structure on their Drinfeld’s double—the double Ringel–Hall.

A key idea in the study of a connected compact Lie group K is the concept of a maximal torus, that is a subgroup T of K that is isomorphic to several copies of and that is not contained in any larger subgroup of this type.

A basic example is the case = (), in which case we may take to be the group of diagonal elements in.A basic result is the torus theorem which states that every element of. Formal definition. Let be a Lie algebra and let be a vector space. We let () denote the space of endomorphisms of, that is, the Integral forms for Weyl modules of GL book of all linear maps of to itself.

We make () into a Lie algebra with bracket given by the commutator: [,] = ∘ − ∘ for all ρ,σ in ().Then a representation of on is a Lie algebra homomorphism: → (). Explicitly, this means that should be a linear map and.

Quantum Schur–Weyl theory refers to a three-level duality relation. At Level I, it investigates a certain double centralizer property, the quantum Schur–Weyl reci-procity, associated with some bimodules of quantum gln and the Hecke algebra (of type A)—the tensor spaces of the natural representation of quantum gln (see [43], [20], [27]).Cited by:   This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics.

Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way.

Lectures on Lie groups and geometry S. Donaldson Ma Abstract These are the notes of the course given in Autumn and Spring Two good books (among many): Adams: Lectures on Lie groups (U. Chicago Press) Fulton and Harris: Representation Theory (Springer) Also various writings of Atiyah, Segal, Bott, Guillemin and.

Update: The question at the end of the paper on integral conjugacy has been answered in the affirmative by G. Nebe, in On conjugacy of diagonalizable integral matrices, arXiv F.

Ihringer, P. Sin and Q. Xiang, New bounds for partial spreads in H(2d-1,q^2) and partial ovoids of the Ree-Tits octagon. Meinolf Geek, Gunter Malle, in Handbook of Algebra, p-adic reflection groups. Let R be an integral domain, L an R-lattice of finite rank, i.e., a torsion-free finitely generated R-module, and W a finite subgroup of GL(L) generated by one can ask under which conditions the invariants of W on the symmetric algebra R[L] of the dual L* are a graded polynomial ring.

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and its algebraic operations (for example, matrix. Chapter Constructing quantum gl.

via quantum Schur algebras § A stabilization property § The BLM algebra K and its canonical basis § The completion Kbof K and multiplication formulas § Embedding U.

v (gl. n) into Kb § Z-forms of U. v (gl. n) § Integral quantum Schur–Weyl. This leads to the subject of "Dirac Cohomology", see the book "Dirac Operators in Representation Theory". Here, instead of working with the Universal Enveloping Algebra and modules for it, one works with the tensor product of this with a Clifford algebra.

Irreducible modules then acquire a spinor representation factor. Tensors and Schur-Weyl duality. Application to 2d bosonization.

Induced representations and Frobenius reciprocity. Survey of matrix groups: GL, SL, SO, SU, Sp etc. De nition of a Lie group. Components, compactness, universal cover. GL and SL. Groups preserving sesquilinear forms. Grassmannians.

Groups preserving symmetric bilinear forms. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums.

This book is designed for mathematicians and physicists, experts and students, all those who want to master the new double Hecke algebra technique. There is now also an algebraic proof available, cf. [K], Theorem So D,(p) > 0 for all p and we can compute D,(p).

Filtrations of Weyl Modules It should be mentioned that there is a direct way of constructing the contravariant form on V(& that does not use the. Part I: Lie Groups Richard Borcherds, Mark Haiman, Nicolai Reshetikhin, Vera Serganova, and Theo Johnson-Freyd October 5, File Size: 1MB. Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N.

Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit, MIT Press, August ; Automorphic Forms and Representations, D. Bump, CUP ; Notes on Fermat's Last Theorem, A.J.

van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced. As an application, we classify the completely splittable representations of general linear groups and give an exact character formula for these modules.

Lowering operators for GL$\mathbf{(n)}$ and quantum GL$\mathbf{(n)}$, in: Group representations: cohomology, group actions and topology (Seattle, WA, ),Proc. Sympos. The simplest description of the toric variety associated to the Weyl chambers of a complex semisimple group G G is that it is the closure of a generic orbit of its maximal complex torus T T in flag variety G / B G/B of G G (here B B is a Borel subgroup).

Thanks!. Maybe Weyl's unitary trick gives another proof of Schur-Weyl duality, but it would probably be neither constructive nor combinatorical in my book (Haar measure!). There are various papers on a combinatorial approach to invariant theory (e.g., D.

Eisenbud, D. De Concini, C. Procesi, Young diagrams and determinantal varieties, which appears to. This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the addition to its accessible.Canonical bases connect quantum Schur-Weyl duality and RSK.

Let V and Vq be Q- and Q(q)-vector spaces, respectively, of dimension dV. The canonical basis of V⊗r q beautifully connects quantum Schur-Weyl duality with the RSK correspondence. Let Uq(gV) be the quantized enveloping algebra of gV:= gl(V) and Hr the type Ar−1 Hecke algebra.