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1

Gelfand-Raikov representations of Coxeter groups associated with positive definite norm functions

Bożejko M., Hirai T.

Probability and Mathematical Statistics

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2014

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Vol. 34, Fasc. 1

161--180

EN

The main purpose of the paper is to study the type of Gelfand-Raikov representations of Coxeter groups (W, S) for the special positive definite functions coming from the deformed Poisson (Haagerup) positive definite functions qL(w) for some special length (norm) functions L on Coxeter groups W.

2

Classical method of constructing a complete set of irreducible representations of semidirect product of a compact group with a finite group

Hirai T.

Probability and Mathematical Statistics

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2013

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Vol. 33, Fasc. 2

353--362

EN

Let G = U x S be a group of semidirect product of U compact and S finite. For an irreducible representation (= IR) ρ of U, let S([ρ]) be the stationary subgroup in S of the equivalence class [ρ] ∈ Û. Intertwining operators Jρ(s) (s ∈ S([ρ])) between ρ and s−1ρ gives in general a spin (= projective) representation of S([ρ]), which is lifted up to a linear representation J′ρ of a covering group S([ρ])′ of S([ρ]). Put π0:= ρ ·J′ρ, and take a spin representation π1 of S([ρ]) corresponding to the factor set inverse to that of Jρ, and put Π(π0, π1) = IndGU x S([ρ]) (π0 ▪ π1). We give a simple proof that Π(π0, π1) is irreducible and that any IR of G is equivalent to some of Π(π0, π1).

3

Transmission electron microscopy in plasma surface interaction in fusion research.

Hirai T., Linke J., Majerus P., Rödig M.

Archives of Materials Science

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2005

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Vol. 26, nr 1-2

89-94

EN

Transmission electron microscopy (TEM) is a powerful method to study the microstructure of plasma facing materials in fusion devices. The main topics that have been presented so far are the observation of radiation damage caused by particle bombardment and the characterization of deposits and dust created in fusion devices and transient heat load events. The present work summarizes the recent TEM works in this field and the possible use of TEM studies in high heat flux testing.