Parahoric induction and chamber homology for SL2

We consider the special linear group G=SL2 over a p-adic field, and its diagonal subgroup M=GL1. Parabolic induction of representations from M to G induces a map in equivariant homology, from the Bruhat-Tits building of M to that of G. We compute this map at the level of chain complexes, and show that it is given by parahoric induction (as defined by J.-F. Dat).Comment: 19 page

Descent of Hilbert C*-modules

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert C*-modules over B. We prove that under certain conditions (which are always satisfied if, for instance, A is nuclear), the image of this functor can be described in terms of coactions of a certain coalgebra canonically associated to F. We then discuss several examples that fit into this framework: parabolic induction of tempered group representations; Hermitian connections on Hilbert C*-modules; Fourier (co)algebras of compact groups; and the maximal C*-dilation of operator modules over non-self-adjoint operator algebras.Comment: 37 pages. Fixed a typo in the definition of curvature in Definition 6.

The Counter Narrative: Reframing Success of High Achieving Black and Latino Males in Los Angeles County

This report highlights young men who are the products of high expectations. We take time to shine a spotlight on the resilient, intelligent, and caring young men across Los Angeles County. This report takes an unapologetic stance in stating that these young men who are thriving in their homes, taking on leadership roles in their schools, and making a difference in their communities. This report is not intended to be full of the doom and gloom about what is wrong with young Black and Latino men. To the contrary, we take the time to center their voices, hear their stories, and listen to their takeaways about how they have accomplished what they are doing and the recommendations that they offer on how to support other Black and Latino young men just like them

A Second Adjoint Theorem for SL(2,R)

We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).Comment: 38 page

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 02: Historical Highlights

The first of three panels in the exhibit that provide general historical highlights about the Dory Fleet, panel two features a timeline of events from 1855 to 1935. It incorporates a section from the Oregon House Calendar of 1927, chronicling the introduction and passage of House Bill 282. This legislation closed the Nestucca River to commercial fishing. The panel also includes an excerpt from the 1927 version of the Oregon Voters’ Pamphlet that describes an initiative to overturn the legislative action.https://digitalcommons.linfield.edu/dory_exhibit/1001/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 13: Blessing of the Fleet

Like many fishing communities, the Pacific City dory community honors its fleet, asks for bountiful and safe fishing for the coming season, and remembers those who have died during the year at the annual Blessing of the Fleet. The ceremony is held on the beach the first Saturday in June. In a similar vein, the community celebrates the dories and honors those who made significant contributions to the fleet and the community during the Memorial Wall Ceremony. This observance normally takes place during Dory Days. Panel 13 describes both of these events.https://digitalcommons.linfield.edu/dory_exhibit/1012/thumbnail.jp

Fredholm modules over graph C*-algebras

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C*-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators; and we exhibit generating Fredholm modules for the K-homology of quantum lens spaces.Comment: 14 page

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 19: The Project - Archives & More

Panel 19 features information about the digital archives created to preserve the history of the Pacific City Dory Fleet. It also documents some of the creative and scholarly work associated with the project done by Linfield students and faculty. It is the third of three exhibit panels that chronicle the Launching through the Surf project.https://digitalcommons.linfield.edu/dory_exhibit/1018/thumbnail.jp