249 research outputs found
Real representations of C2-graded groups : the linear and Hermitian theories
No full textWe study linear and hermitian representations of finite C2-graded groups. We prove that the category of linear representations is equivalent to a category of antilinear representations as an infinity-category. We also prove that the category hermitian representations, as an ∞-category, is equivalent to a category of usual representations
Real representations of C2-graded groups : the antilinear theory
No full textWe use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C2-graded groups. A finite C2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial component of the theory. Among other things, we study characters and Frobenius-Schur indicators. As an example, we describe the antilinear representations of the C2-graded group An≤Sn
Brauer's 14th Problem and Dyson's Tenfold Way
No full textWe consider Brauer's 14th Problem in the context of "Real" structures on
finite groups and their antilinear representations. The problem is to count the
number of characters of different type using "group theory". While Brauer's
original problem deals only with the three types (real, complex and
quaternionic), here we consider the ten types coming from Dyson's tenfold way
Subregular representations of Sln and simple singularities of type An-1. Part II
No full textThe aim of this paper is to show that the structures on K-theory
used to formulate Lusztig's conjecture for subregular nilpotent sln-representations
are, in fact, natural in the McKay correspondence. The main result is a
categorification of these structures. The no-cycle algebra plays the special role
of a bridge between complex geometry and representation theory in positive
characteristic
Electronic spectroscopy of carbon chain radicals using cw cavity ring down in conjunction with mass detection
No full textThe electronic absorption spectrum of the 2A'' − X 2A'' origin band of the
nonlinear carbon chain radical C6H4
+ was rotationally resolved by cw-CRD
spectroscopy [41]. It was analysed using a least-squares method and the rotational
constants of the ground and excited states were determined accurately. The 581 nm
band observed under the same discharge conditions is assigned to the same electronic
transition of C6H4
+ but involving the excitation of the ν12 vibrational mode in the
upper state based on comparison with ab initio results. The presented data provide a
basis for future observations of the C6H4
+ radical in both millimeter and infrared
regions.
A linear time-of-flight mass spectrometer was constructed to provide on-line
monitoring of the plasma discharge with a mass resolution of 1 amu at a range up to
120 amu. The results from the acetylene/helium plasma discharge are in good
agreement with those obtained using the reflectron TOF mass spectrometer and a
similar ion source [42]. To improve the experimental set-up, the following
modifications can be made:
• Transferring the signal from the oscilloscope directly to a PC via a
GPIB card will increase the speed of data processing;
• Computer control of the voltage applied will make the spectrometer
easier to operate;
• Using a metal grid at ground potential in front of MCP detector will
increase the flight time of ions improving the mass resolution;
• Installing a focusing lens will increase the number of ions arriving at
the detector, and therefore increase the signal on the oscilloscope
Kac-Moody groups and their representations
No full textIn this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open questions
A second greek account of the revolution of a) Pseudo-Dmitriy (Russia, 1605-1606) : Codex Iviron 710, ff. 100rv
No full textThe author publishes, with commentary and english translation, the text of the Διήγησις περ'ι τής έν ’Ρωσία έπαναστάσεως τοϋ ψενδο - Δημητρίον (An account of the revolution of pseudo-Dmitriy, untitled), Codex Iviron 710, ff. 100rv, which recounts certain events relating to the activity ofthe first pseudoDmitriy (1605-1606)
Duality for Hopf Algebroids
No full textAbstractOur goal is twofold. First, we formulate a duality between commutative bialgebroids and cocommutative bialgebras over a ring extension. Second, we show that for a certain action groupoid J, the Hopf algebroid of functions on the Frobenius kernel J1 is dual to the restricted enveloping algebra of the Lie algebroid of J
2-groups, 2-characters, and Burnside rings
No full textWe study 2-representations, i.e., actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter–Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno's formula for the Ganter–Kapranov 2-character of a finite group
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