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Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 224/5 ( reviews)

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Book Synopsis Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character by : Ping-Shun Chan

Download or read book Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character written by Ping-Shun Chan. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 204, number 957 (first of 5 numbers)."

Invariant Representations of GSp(2)

2005 Automorphic forms
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Release : 2005
Genre : Automorphic forms
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Invariant Representations of GSp(2) by : Ping-Shun Chan

Download or read book Invariant Representations of GSp(2) written by Ping-Shun Chan. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Let F be a number field or a p-adic field. We introduce in Chapter 2 of this work two reductive rank one F-groups, H1, H2, which are twisted endoscopic groups of GSp(2) with respect to a fixed quadratic character [epsilon] of the idèle class group of F if F is global, F[superscript X] if F is local. If F is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of H1, H2 to those of GSp(2). In Chapter 4, we establish this lifting in terms of the Satake parameters which parametrize the automorphic representations. By means of this lifting we provide a classification of the discrete spectrum automorphic representations of GSp(2) which are invariant under tensor product with [epsilon]. The techniques through which we arrive at our results are inspired by those of Kazhdan's in [K]. In particular, they involve comparing the spectral sides of the trace formulas for the groups under consideration. We make use of the twisted extension of Arthur's trace formula, and Kottwitz-Shelstad's stabilization of the elliptic component of the geometric side of the twisted trace formula. If F is local, in Chapter 5 we provide a classification of the irreducible admissible representations of GSp(2, F) which are invariant under tensor product with the quadratic character [epsilon] of F[superscript X]. Here, our techniques are also directly inspired by [K]. More precisely, we use the global results from Chapter 4 to express the twisted characters of these invariant representations in terms of the characters of the admissible representations of H[subscript i](F) (i = 1, 2). These (twisted) character identities provide candidates for the liftings predicted by the local component of the conjectural Langlands functoriality. The proofs rely on Sally-Tadić's classification of the irreducible admissible representations of GSp(2, F), and Flicker's results on the lifting from PGSp(2) to PGL(4).

Automorphic Forms and Shimura Varieties of PGSp (2)

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 322/5 ( reviews)

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Book Synopsis Automorphic Forms and Shimura Varieties of PGSp (2) by : Yuval Z. Flicker

Download or read book Automorphic Forms and Shimura Varieties of PGSp (2) written by Yuval Z. Flicker. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."

Unfolding CR Singularities

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

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Book Synopsis Unfolding CR Singularities by : Adam Coffman

Download or read book Unfolding CR Singularities written by Adam Coffman. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 962 (first of 5 numbers)."

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 694/5 ( reviews)

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Book Synopsis Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups by : Ross Lawther

Download or read book Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups written by Ross Lawther. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

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