Hall algebras and quantum symmetric pairs I: Foundations

A quantum symmetric pair consists of a quantum group $\mathbf U$ and its coideal subalgebra ${\mathbf U}^{\imath}_{\varsigma}$ with parameters $\varsigma$ (called an $\imath$quantum group). We initiate a Hall algebra approach for the categorification of $\imath$quantum groups. A universal $\imath$quantum group $\widetilde{\mathbf U}^{\imath}$ is introduced and ${\mathbf U}^{\imath}_{\varsigma}$ is recovered by a central reduction of $\widetilde{\mathbf U}^{\imath}$. The modified Ringel-Hall algebras of the first author and Peng, which are closely related to semi-derived Hall algebras of Gorsky and motivated by Bridgeland's work, are extended to the setting of 1-Gorenstein algebras, as shown in Appendix~A by the first author. A new class of 1-Gorenstein algebras (called $\imath$quiver algebras) arising from acyclic quivers with involutions is introduced. The modified Ringel-Hall algebras for the Dynkin $\imath$quiver algebras are shown to be isomorphic to the universal quasi-split $\imath$quantum groups of finite type, and a reduced version provides a categorification of ${\mathbf U}^{\imath}_{\varsigma}$. Monomial bases and PBW bases for these Hall algebras and $\imath$quantum groups are constructed. In the special case of quivers of diagonal type, our construction reduces to a reformulation of Bridgeland's Hall algebra realization of quantum groups.Comment: 75 pages, a dozen of figure

The translation of Indonesian Passive Voice into English in Novel 9 Summers 10 Autumns by Iwan Setyawan translated by Maggie Tiojakin

Desi Amalia. 1155030043. The Translation of Indonesian Passive Voice Into English In Novel 9 Summers 10 Autumns by Iwan Setawan Translated by Maggie Tiojakin. Thesis for English Literature in Adab and Humanities Faculty, State Islamic University of Sunan Gunung Djati Bandung, 2019. This research is done to find out the corresponding equivalents of Indonesian passive constructions in English as used in the novel and its translation an to identify the method of translation when translate SL into TL so that the TL sounds natural. The steps and procedures of discovering the answer to the both of research problems are shown under the discussion of research method which includes: (1) the data source, (2) method and technique of collecting the data consisting of observation method and note-taking technique; (3) method and technique of analyzing the data. The results of the study show that among the passive in Indonesian which can be identified in SL, most are marked by prefix di- (prefix di- + verb base) and (prefix di- + verb base + suffix –kan, -i), and prefix ter-, which are also translated into passive in English (be + past participle ) with five types namely (be+ past participle) + to infinitive translation, (be+ past participle) + by agent translation (stated and implied) , the next is translated into active, and the rest translated into get/got + past participle. This clearly reveals that some passives in SL are retained, namely translated into passive in English and some others are translated into actives. Second, from the 684 data analysis the researcher found four types of translation methods or procedures used in the passive translation, namely 33 sentences are translated using literal translation, 21 sentences are translated using transposition, 17 sentences are translated using modulation, and 13 sentences are translated using adaptation. From the analysis it also clearly shows that most of the passive voice in the Novel used literal translation to get the equivalent of the meaning

ı\imathHall algebra of Jordan quiver and ı\imathHall-Littlewood functions

We show that the $\imath$Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this $\imath$Hall algebra to the ring of symmetric functions in two parameters $t, \theta$, which maps the $\imath$Hall basis to a class of (modified) inhomogeneous Hall-Littlewood ($\imath$HL) functions. The (modified) $\imath$HL functions admit a formulation via raising and lowering operators. We formulate and prove Pieri rules for (modified) $\imath$HL functions. The modified $\imath$HL functions specialize at $\theta=0$ to the modified HL functions; they specialize at $\theta=1$ to the deformed universal characters of type C, which further specialize at $(t=0, \theta =1)$ to the universal characters of type C.Comment: v2,41 pages,references adde

Thermocline fluctuations in the equatorial Pacific related to the two types of El Niño events

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 30 (2017): 6611-6627, doi:10.1175/JCLI-D-16-0291.1.The interannual fluctuations of the equatorial thermocline are usually associated with El Niño activity, but the linkage between the thermocline modes and El Niño is still under debate. In the present study, a mode function decomposition method is applied to the equatorial Pacific thermocline, and the results show that the first two dominant modes (M1 and M2) identify two distinct characteristics of the equatorial Pacific thermocline. The M1 reflects a basinwide zonally tilted thermocline related to the eastern Pacific (EP) El Niño, with shoaling (deepening) in the western (eastern) equatorial Pacific. The M2 represents the central Pacific (CP) El Niño, characterized by a V-shaped equatorial Pacific thermocline (i.e., deep in the central equatorial Pacific and shallow on both the western and eastern boundaries). Furthermore, both modes are stable and significant on the interannual time scale, and manifest as the major feature of the thermocline fluctuations associated with the two types of El Niño events. As good proxies of EP and CP El Niño events, thermocline-based indices clearly reveal the inherent characteristics of subsurface ocean responses during the evolution of El Niño events, which are characterized by the remarkable zonal eastward propagation of equatorial subsurface ocean temperature anomalies, particularly during the CP El Niño. Further analysis of the mixed layer heat budget suggests that the air–sea interactions determine the establishment and development stages of the CP El Niño, while the thermocline feedback is vital for its further development. These results highlight the key influence of equatorial Pacific thermocline fluctuations in conjunction with the air–sea interactions, on the CP El Niño.This work is jointly supported by the Funds for Creative Research Groups of China (Grant 41521005), the Special Fund for Public Welfare Industry (GYHY201506013), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA11010301), and the National Natural Science Foundation of China (Grants 41406033, 41475057, 41376024, 41676013) and the CAS/SAFEA International Partnership Program for Creative Research Teams.2018-01-2