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HOMOTOPY FIXED POINT SETS AND ACTIONS ON HOMOGENEOUS SPACES OF p-COMPACT GROUPS
Kenshi Ishiguro,Lee, Hyang-Sook Korean Mathematical Society 2004 대한수학회지 Vol.41 No.6
We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.
INVARIANT RINGS AND DUAL REPRESENTATIONS OF DIHEDRAL GROUPS
Kenshi Ishiguro 대한수학회 2010 대한수학회지 Vol.47 No.2
The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory,the rational cohomology of a classifying space is a ring of invariants,which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.
Modular invariants under the actions of some reflection groups related to Weyl groups
Kenshi Ishiguro,Takahiro Koba,Toshiyuki Miyauchi,Erika Takigawa 대한수학회 2020 대한수학회보 Vol.57 No.1
Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group $G$ with a maximal torus $T$ is expressed as the ring of invariants, $H^*(BG; \Q)\cong H^*(BT; \Q)^{W(G)}$, which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod $p$ reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups $Sp(n)$ and for the alternating groups $A_n$ as the subgroup of $W(SU(n))$. We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod $p$ cohomology of a space. For $n=3, 4$, the rings under a conjugate of $W(Sp(n))$ are shown to be polynomial, and for $n=6, 8$, they are non--polynomial. The structures of $H^*(BT^{n-1}; \F_p)^{A_n}$ will be also discussed for $n=3, 4$.
MODULAR INVARIANTS UNDER THE ACTIONS OF SOME REFLECTION GROUPS RELATED TO WEYL GROUPS
Ishiguro, Kenshi,Koba, Takahiro,Miyauchi, Toshiyuki,Takigawa, Erika Korean Mathematical Society 2020 대한수학회보 Vol.57 No.1
Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)<sup>W(G)</sup>, which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A<sub>n</sub> as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT<sup>n-1</sup>; 𝔽<sub>p</sub>)<sup>A<sub>n</sub></sup> will be also discussed for n = 3, 4.
INVARIANT RINGS AND DUAL REPRESENTATIONS OF DIHEDRAL GROUPS
Ishiguro, Kenshi Korean Mathematical Society 2010 대한수학회지 Vol.47 No.2
The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.
INTERPRETATION OF (596) SCHEILA'S TRIPLE DUST TAILS
Ishiguro, Masateru,Hanayama, Hidekazu,Hasegawa, Sunao,Sarugaku, Yuki,Watanabe, Jun-ichi,Fujiwara, Hideaki,Terada, Hiroshi,Hsieh, Henry H.,Vaubaillon, Jeremie J.,Kawai, Nobuyuki,Yanagisawa, Kenshi,Kuro IOP Publishing 2011 ASTROPHYSICAL JOURNAL LETTERS - Vol.741 No.1
<P>Strange-looking dust cloud around asteroid (596) Scheila was discovered on 2010 December 11.44-11.47. Unlike normal cometary tails, it consisted of three tails and faded within two months. We constructed a model to reproduce the morphology of the dust cloud based on the laboratory measurement of high-velocity impacts and the dust dynamics. As a result, we succeeded in reproducing the peculiar dust cloud by an impact-driven ejecta plume consisting of an impact cone and downrange plume. Assuming an impact angle of 45 degrees, our model suggests that a decameter-sized asteroid collided with (596) Scheila from the direction of (alpha(im), delta(im)) = (60 degrees, -40 degrees) in J2000 coordinates on 2010 December 3. The maximum ejection velocity of the dust particles exceeded 100 m s(-1). Our results suggest that the surface of (596) Scheila consists of materials with low tensile strength.</P>
OBSERVATIONAL EVIDENCE FOR AN IMPACT ON THE MAIN-BELT ASTEROID (596) SCHEILA
Ishiguro, Masateru,Hanayama, Hidekazu,Hasegawa, Sunao,Sarugaku, Yuki,Watanabe, Jun-ichi,Fujiwara, Hideaki,Terada, Hiroshi,Hsieh, Henry H.,Vaubaillon, Jeremie J.,Kawai, Nobuyuki,Yanagisawa, Kenshi,Kuro IOP Publishing 2011 ASTROPHYSICAL JOURNAL LETTERS - Vol.740 No.1
<P>An unexpected outburst was observed around (596) Scheila in 2010 December. We observed (596) Scheila soon after the impact using ground-based telescopes. We succeeded in the detection of a faint linear tail after 2011 February, which provides a clue to determine the dust ejection date. It is found that the dust particles ranging from 0.1-1 mu m to 100 mu m were ejected into the interplanetary space impulsively on December 3.5 +/- 1.0 day. The ejecta mass was estimated to be (1.5-4.9) x 10(8) kg, suggesting that an equivalent mass of a 500-800 m diameter crater was excavated by the event. We also found that the shape of the light curve changed after the impact event probably because fresh material was excavated around the impact site. We conclude that a decameter-sized asteroid collided with (596) Scheila only eight days before the discovery.</P>
MULTIBAND OPTICAL OBSERVATION OF THE P/2010 A2 DUST TAIL
Kim, Junhan,Ishiguro, Masateru,Hanayama, Hidekazu,Hasegawa, Sunao,Usui, Fumihiko,Yanagisawa, Kenshi,Sarugaku, Yuki,Watanabe, Jun-ichi,Yoshida, Michitoshi IOP Publishing 2012 ASTROPHYSICAL JOURNAL LETTERS - Vol.746 No.1
<P>An inner main-belt asteroid, P/2010 A2, was discovered on 2010 January 6. Based on its orbital elements, it is considered that the asteroid belongs to the Flora collisional family, where S-type asteroids are common, while showing a comet-like dust tail. Although analysis of images taken by the Hubble Space Telescope and Rosetta spacecraft suggested that the dust tail resulted from a recent head-on collision between asteroids, an alternative idea of ice sublimation was suggested based on the morphological fitting of ground-based images. Here, we report a multiband observation of P/2010 A2 made on 2010 January with a 105 cm telescope at the Ishigakijima Astronomical Observatory. Three broadband filters, g', R-c, and I-c, were employed for the observation. The unique multiband data reveal that the reflectance spectrum of the P/2010 A2 dust tail resembles that of an Sq-type asteroid or that of ordinary chondrites rather than that of an S-type asteroid. Due to the large error of the measurement, the reflectance spectrum also resembles the spectra of C-type asteroids, even though C-type asteroids are uncommon in the Flora family. The reflectances relative to the g' band (470 nm) are 1.096 +/- 0.046 at the R-c band (650 nm) and 1.131 +/- 0.061 at the I-c band (800 nm). We hypothesize that the parent body of P/2010 A2 was originally S-type but was then shattered upon collision into scattering fresh chondritic particles from the interior, thus forming the dust tail.</P>
Optical and Near-infrared Polarimetry of Non-periodic Comet C/2013 US10 (Catalina)
Kwon, Yuna Grace,Ishiguro, Masateru,Kuroda, Daisuke,Hanayama, Hidekazu,Kawabata, Koji S.,Akitaya, Hiroshi,Nakaoka, Tatsuya,Itoh, Ryosuke,Toda, Hiroyuki,Yanagisawa, Kenshi,Lee, Myung Gyoon,Ohta, Kouji American Institute of Physics 2017 The Astronomical journal Vol.154 No.4
<P>We present an optical and near-infrared (hereafter NIR) polarimetric study of a comet C/2013 US10 (Catalina) observed on UT 2015 December 17-18 at phase angles of alpha - 52 degrees.1-53 degrees.1. Additionally, we obtained an optical spectrum and multi-band images to examine the influence of gas emission. We find that the observed optical signals are significantly influenced by gas emission; that is, the gas-to-total intensity ratio varies from 5 to 30% in the RC and 3%-18% in the I-C bands, depending on the position in the coma. We derive the 'gas-free dust polarization degrees' of 13.8% +/- 1.0% in the RC and 12.5% +/- 1.1% in the IC bands and a gray polarimetric color, i.e., -8.7% +/- 9.9% mu m(-1) in optical and 1.6% +/- 0.9% mu m(-1) in NIR. The increments of polarization obtained from the gas correction show that the polarimetric properties of the dust in this low-polarization comet are not different from those in high-polarization comets. In this process, the cometocentric distance dependence of polarization has disappeared. We also find that the RC-band polarization degree of the southeast dust tail, which consists of large dust particles (100 mu m(-1) mm), is similar to that in the outer coma where small and large ones are mixed. Our study confirms that the dichotomy of cometary polarization does not result from the difference of dust properties, but from depolarizing gas contamination. This conclusion can provide a strong support for similarity in origin of comets.</P>