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Chapter
Polynomial Conjectures
The aim of this chapter is to present two conjectures which are interesting and still open (cf. Baklouti and Ludwig (Monatsh Math 134:19–37, 2001), Baklouti et al. (Bull Sci Math 129:187–209, 2005), Corwin and...
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Chapter
Monomial Representations of Discrete Type of Exponential Solvable Lie Groups
When investigating a concrete problem in the representation theory of solvable Lie groups, it is easy to realize that we have enough tools only for the nilpotent case. Here we shall consider Penney’s Planchere...
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Chapter
Intertwining Operators for Irreducible Representations of an Exponential Solvable Lie Group
When we study problems in representation theory, it is often very useful to construct an intertwining operator between two equivalent unitary representations. A prototype arises in the following situation. Let ...
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Chapter
Variants of Plancherel Formulas for Monomial Representations of Exponential Solvable Lie Groups
Let π be a unitary representation of a connected Lie group G acting on a Hilbert space H ...
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Chapter
Holomorphically Induced Representations of Solvable Lie Groups
Once we leave the exponential picture, we know the fundamental results by Auslander-Kostant and Pukanszky. Here we study some intertwining operators and real polarizations. First, let
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Chapter
Bounded Irreducible Representations
Let be an exponential solvable Lie group. In this chapter we characterize bounded, topologically irreducible Banach-space representations of G using tr...
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Chapter
Branching Laws and the Multiplicity Function of Unitary Representations of Exponential Solvable Lie Groups
Throughout the chapter G denotes an exponential solvable Lie group. Let A and H be two closed connected subgroups of G and π and σ unitary and irreducible representations of G and H respectively. Branching laws a...
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Chapter
Intertwining Operators of Induced Representations and Restrictions of Representations of Exponential Solvable Lie Groups
One of the most important problems in the disintegration theory of group representations is to write down explicit unitary operators that intertwine unitary representations and their decomposition into irreduc...
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Chapter and Conference Paper
Monomial Representations of Discrete Type of an Exponential Solvable Lie Group
Let G be an exponential solvable Lie group, H an analytic subgroup of G and \(\chi \) a unitary character of H. We study some p...
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Article
Graft placement with an omental flap for ruptured infective common iliac aneurysm in a patient with a continuous flow left ventricular assist device: alternative surgical approach avoiding driveline injury and pathogen identification by 16S ribosomal DNA gene analysis
Patients supported by mechanical circulatory support have to wait for longer periods for heart transplantation in Japan. Infective events are a major complication and influence survival. Here, we present the c...
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Book
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Chapter
Commutativity Conjecture: Restriction Case
As Frobenius reciprocity suggests, there is a kind of duality between the induction and the restriction of representations. Under this guiding principle, let us formulate and prove for the restriction of repre...
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Chapter
Haar Measure and Group Algebra
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Chapter
Four Exponential Solvable Lie Groups
The group ( ℝ n ...
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Chapter
Kirillov Theory for Nilpotent Lie Groups
In this chapter, we examine in detail the Kirillov theory for nilpotent Lie groups, which are always assumed to be connected and simply connected.
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Chapter
Irreducible Decomposition
>As usual let G = exp 𝔤 $$G = \text{exp}\ \mathfr...
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Chapter
Frobenius Reciprocity
Let G be a σ-compact Lie group with Lie algebra 𝔤 \(\mathfrak{g}\) , and we only consider unitary representations π whose Hilbert space ℋ π \(\mathcal{H}_{\pi }\) are separable. First we reme...
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Chapter
Commutativity Conjecture: Induction Case
Let G be a connected and simply connected nilpotent Lie group with Lie algebra 𝔤 \(\mathfrak{g}\) an...
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Chapter
Preliminaries: Lie Groups and Lie Algebras
There are many texts on Lie groups and Lie algebras. Here following Sugiura [74] we gather general preliminaries. As other references we list [45, 62, 70, 71].
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Chapter
Induced Representations
Let G be a locally compact group and H a closed subgroup of G. We are going to show that there exists a G-invariant Borel measure on the quotient space G∕H, if and only if for the modular functions Δ ...