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Abstract. Let 𝘎 be a real semisimple algebraic Lie group and 𝘏 a real reductive algebraic subgroup. We describe the pairs (𝘎,𝘏) for which the representation of 𝘎 in L²(𝘎/𝘏) is tempered. The proof gives the complete list of pairs (𝘎,𝘏) for which L²(𝘎/𝘏) is not tempered. When 𝘎 and 𝘏 are complex Lie groups, the temperedness condition is characterized by the fact that 𝘵𝘩𝘦 𝘴𝘵𝘢𝘣𝘪𝘭𝘪𝘻𝘦𝘳 𝘪𝘯 𝘏 𝘰𝘧 𝘢 𝘨𝘦𝘯𝘦𝘳𝘪𝘤 𝘱𝘰𝘪𝘯𝘵 𝘰𝘯 𝘎/𝘏 𝘪𝘴 𝘷𝘪𝘳𝘵𝘶𝘢𝘭𝘭𝘺 𝘢𝘣𝘦𝘭𝘪𝘢𝘯. 𝘔𝘢𝘵𝘩𝘦𝘮𝘢𝘵𝘪𝘤𝘴 𝘚𝘶𝘣𝘫𝘦𝘤𝘵 𝘊𝘭𝘢𝘴𝘴𝘪𝘧𝘪𝘤𝘢𝘵𝘪𝘰𝘯: Primary 22𝐄46; secondary 43𝐀85, 22𝐅30. 𝘒𝘦𝘺 𝘞𝘰𝘳𝘥𝘴: Lie groups, homogeneous spaces, tempered representations, unitary representations, matrix coefficients, symmetric spaces. 

Abstract Kondo lattice materials, where localized magnetic moments couple to itinerant electrons, provide a very rich backdrop for strong electron correlations. They are known to realize many exotic phenomena, with a dramatic example being recent observations of quantum oscillations and metallic thermal conduction in insulators, implying the emergence of enigmatic charge-neutral fermions. Here, we show that thermal conductivity and specific heat measurements in insulating YbIr 3 Si 7 reveal emergent neutral excitations, whose properties are sensitively changed by a field-driven transition between two antiferromagnetic phases. In the low-field phase, a significant violation of the Wiedemann-Franz law demonstrates that YbIr 3 Si 7 is a charge insulator but a thermal metal. In the high-field phase, thermal conductivity exhibits a sharp drop below 300 mK, indicating a transition from a thermal metal into an insulator/semimetal driven by the magnetic transition. These results suggest that spin degrees of freedom directly couple to the neutral fermions, whose emergent Fermi surface undergoes a field-driven instability at low temperatures. 

Super-Kamiokande (SK) has observed ${}^8\mathrm{B}$solar neutrino elastic scattering at recoil electron kinetic energies ( $E_{\mathrm{kin}}$) as low as 3.49 MeV to study neutrino flavor conversion within the Sun. At SK-observable energies, these conversions are dominated by the Mikheyev-Smirnov-Wolfenstein effect. An upturn in the electron neutrino survival probability in which vacuum neutrino oscillations become dominant is predicted to occur at lower energies, but radioactive background increases exponentially with decreasing energy. New machine learning approaches provide substantial background reduction below 3.49 MeV such that statistical extraction of solar neutrino interactions becomes feasible. This article presents an analysis of the solar neutrino interaction rate at $E_{\mathrm{kin}}<3.49\mathrm{MeV}$with the full SK-IV period, using data from a wideband intelligent trigger when available and with a boosted decision tree for event selection. A solar neutrino signal is observed between $2.99\mathrm{MeV}<E_{\mathrm{kin}}<3.49\mathrm{MeV}$with $2.76\sigma$significance and a data to unoscillated Monte Carlo ratio of ${0.307}_{-0.111}^{+0.112}$. These additional low-energy data have a negligible effect on the $1\sigma$intervals of the fits to the solar neutrino energy spectrum but have a noticeable effect on the best fit when using the exponential parametrization. 

Properties of the nuclear equation of state (EoS) can be probed by measuring the dynamical properties of nucleus-nucleus collisions. In this study, we present the directed flow (v1), elliptic flow (v2) and stopping (VarXZ) measured in fixed target Sn+ Sn collisions at 270AMeV with the S'll'RlT Time Projection Chamber. We perform Bayesian analyses in which EoS parameters are var­ied simultaneously within the Improved Quantum Molecular Dynamics-Skyrme (ImQMD-Sky) transport code to obtain a multivariate correlated constraint. The varied parameters include symmetry energy, S0, and slope of the symme­try energy, L, at saturation density, isoscalar effective mass, m;/mN, isovector effective mass, m􀀒/mN and the in-medium cross-section enhancement factor rJ. We find that the flow and VarXZ observables are sensitive to the splitting of proton and neutron effective masses and the in-medium cross-section. Compar­isons of ImQMD-Sky predictions to the S'll' RJT data suggest a narrow range of preferred values for m;/mN, m􀀕/mN and 1/· 

We present the results of searches for nucleon decays via $p\to \nu {\pi }^{+}$and $n\to \nu {\pi }^0$using a $0.484\mathrm{Mt}·\mathrm{yr}$exposure of Super-Kamiokande I-V data covering the entire pure water phase of the experiment. Various improvements on the previous 2014 nucleon decay search [], which used an exposure of $0.173\mathrm{Mt}·\mathrm{yr}$, are incorporated. The physics models related to pion production and nuclear interaction are refined with external data, and a more comprehensive set of systematic uncertainties, now including those associated with the atmospheric neutrino flux and pion production channels, is considered. Also, the fiducial volume has been expanded by 21%. No significant indication of a nucleon decay signal is found beyond the expected background. Lower bounds on the nucleon partial lifetimes are determined to be $3.5\times {10}^{32}\mathrm{yr}$for $p\to \nu {\pi }^{+}$and $1.4\times {10}^{33}\mathrm{yr}$for $n\to \nu {\pi }^0$at 90% confidence level. 

In recent neutrino detectors, neutrons produced in neutrino reactions play an important role. Muon capture on oxygen nuclei is one of the processes that produce neutrons in water Cherenkov detectors. We measured neutron multiplicity in the process using cosmic ray muons that stop in the gadolinium-loaded Super-Kamiokande detector. For this measurement, neutron detection efficiency is obtained with the muon capture events followed by gamma rays to be ${50.2}_{-2.1}^{+2.0}\%$. By fitting the observed multiplicity considering the detection efficiency, we measure neutron multiplicity in muon capture as $P\left(0\right)=24\pm 3\%$, $P\left(1\right)=70_{-2}^{+3}\%$, $P\left(2\right)=6.1\pm 0.5\%$, $P\left(3\right)=0.38\pm 0.09\%$. This is the first measurement of the multiplicity of neutrons associated with muon capture on oxygen without neutron energy threshold. 

Abstract In 2024, a failed supernova (SN) candidate, M31-2014-DS1, was reported in the Andromeda galaxy (M31), located at a distance of approximately 770 kpc. In this Letter, we search for neutrinos from this failed SN using data from Super-Kamiokande (SK). Based on the estimated time of black hole formation inferred from optical and infrared observations, we define a search window for neutrino events in the SK data. Using this window, we develop a dedicated analysis method for failed SNe and apply it to M31-2014-DS1, by conducting a cluster search using the timing and energy information of candidate events. No significant neutrino excess is observed within the search region. Consequently, we place an upper limit on the time-integrated electron antineutrino luminosity from M31-2014-DS1 and discuss its implications for various failed SN models and their neutrino emission characteristics. Despite the 18 MeV threshold adopted to suppress backgrounds, the search remains sufficiently sensitive to constrain the Shen-TM1 equation of state, in a more optimistic emission scenario with progenitor stars of 40M_⊙and relatively high mean electron-antineutrino energies of about 23.2 MeV, yielding a 90% confidence level upper limit of 1.76 × 10⁵³erg on the time-integrated electron antineutrino luminosity, moderately above the expected value of 1.35 × 10⁵³erg. 

We searched for bound neutron decay via $n\to \overline{\nu }+K^0$predicted by the grand unified theories in $0.401\mathrm{Mton}·\mathrm{years}$exposure of all pure water phases in the Super-Kamiokande detector. About 4.4 times more data than in the previous search have been analyzed by a new method including a spectrum fit to kaon invariant mass distributions. No significant data excess has been observed in the signal regions. As a result of this analysis, we set a lower limit of $7.8\times {10}^{32}\mathrm{years}$on the neutron lifetime at a 90% confidence level. 

Measurement of the branching ratio of 16N, 15C, 12B, and 13B isotopes through the nuclear muon capture reaction in the Super-Kamiokande detector