Alcove path model for B(∞)B(\infty)

We construct a model for $B(\infty)$ using the alcove path model of Lenart and Postnikov. We show that the continuous limit of our model recovers a dual version of the Littelmann path model for $B(\infty)$ given by Li and Zhang. Furthermore, we consider the dual version of the alcove path model and obtain analogous results for the dual model, where the continuous limit gives the Li and Zhang model.Comment: 19 pages, 7 figures; improvements from comments, added more figure

A uniform realization of the combinatorial RR-matrix

Kirillov-Reshetikhin crystals are colored directed graphs encoding the structure of certain finite-dimensional representations of affine Lie algebras. A tensor products of column shape Kirillov-Reshetikhin crystals has recently been realized in a uniform way, for all untwisted affine types, in terms of the quantum alcove model. We enhance this model by using it to give a uniform realization of the combinatorial $R$-matrix, i.e., the unique affine crystal isomorphism permuting factors in a tensor product of KR crystals. In other words, we are generalizing to all Lie types Sch\"utzenberger's sliding game (jeu de taquin) for Young tableaux, which realizes the combinatorial $R$-matrix in type $A$. Our construction is in terms of certain combinatorial moves, called quantum Yang-Baxter moves, which are explicitly described by reduction to the rank 2 root systems. We also show that the quantum alcove model does not depend on the choice of a sequence of alcoves joining the fundamental one to a translation of it.Comment: arXiv admin note: text overlap with arXiv:1112.221

A generalization of the alcove model and its applications

The alcove model of the first author and A. Postnikov uniformly describes highest weight crystals of semisimple Lie algebras. We construct a generalization, called the quantum alcove model. In joint work of the first author with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, this was shown to uniformly describe tensor products of column shape Kirillov-Reshetikhin crystals in all untwisted affine types; moreover, an efficient formula for the corresponding energy function is available. In the second part of this paper, we specialize the quantum alcove model to types $A$ and $C$. We give explicit affine crystal isomorphisms from the specialized quantum alcove model to the corresponding tensor products of column shape Kirillov-Reshetikhin crystals, which are realized in terms of Kashiwara-Nakashima columns.Comment: Ver2: Replaced extended abstract with full paper Ver3: Introduction and abstract expanded and made sharper. Signature rule in types A and C had small inaccuracies. Proposition 2.9, more on perfect crystals. Expanded the main Theorem 3.8 (and its proof). Expanded the "Main applications" section. Some changes in the proofs of Prop. 4.14-4.1

Reverse total shoulder replacement for patients with "weight-bearing" shoulders.

Reverse total shoulder arthroplasty (rTSA) has gained popularity in recent years and is indicated for a wide variety of shoulder pathologies. However, use of rTSA in patients with "weight-bearing" shoulders that support wheelchair use or crutches has higher risk. The aim of this study was to assess the results of rTSA in such patients. Between 2005 and 2014, 24 patients (30 shoulders) with weight-bearing shoulders were treated with rTSA at our unit. Patients had cuff arthropathy (n=21), rheumatoid arthritis (n=3), osteoarthritis (n=1), acute fracture (n=3), or fracture sequela (n=2). Postoperatively, patients were advised not to push themselves up and out of their wheelchair for 6 weeks. The study surgeries were performed in 2016, and 21 patients (27 shoulders) who were available for a mean follow-up of 5.6 years (range, 2-10 years). The mean age on surgery day was 78 years (range, 54-90 years). Constant-Murley score improved from 9.4 (range, 2-26) preoperatively to 59.8 (range, 29-80) at the final follow-up (P=0.001). Pain improved from 2/15 (range, 0-8) to 13.8/15 (range, 9-15) (P=0.001). Patient satisfaction (Subjective Shoulder Value) improved from 0.6/10 to 8.7/10 (P=0.001) at final follow-up. Significant improvement in mean range of motion from 46° to 130° of elevation, 13° to 35° of external rotation, and 29° to 78° internal rotation was recorded (P=0.001). Final mean Activities of Daily Living External and Internal Rotation was 32.4/36 (range, 16-36). There were three patients with Sirveaux-Nerot grade-1 (10%) glenoid notching and three with grade 2 (10%). rTSA can be used for treatment of patients with weight-bearing shoulders. Such patients reported pain free movement, resumed daily activities, and high satisfaction rates

A uniform realization of the combinatorial RR-matrix

Kirillov-Reshetikhin (KR) crystals are colored directed graphs encoding the structure of certain finite-dimensional representations of affine Lie algebras. A tensor product of column shape KR crystals has recently been realized in a uniform way, for all untwisted affine types, in terms of the quantum alcove model. We enhance this model by using it to give a uniform realization of the combinatorial $R$-matrix, i.e., the unique affine crystal isomorphism permuting factors in a tensor product of KR crystals. In other words, we are generalizing to all Lie types Schützenberger’s sliding game (jeu de taquin) for Young tableaux, which realizes the combinatorial $R$-matrix in type $A$. We also show that the quantum alcove model does not depend on the choice of a sequence of alcove

A generalization of the alcove model and its applications

The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function

Bilateral femoral neck fractures due to transient osteoporosis of pregnancy: a case report

We describe a case of bilateral femoral neck fractures secondary to transient osteoporosis of pregnancy, which were diagnosed after delivery due to the desire to avoid ionising radiation. These fractures were presumed to be secondary to transient osteoporosis of pregnancy and were treated successfully with internal fixation despite delayed presentation. We discuss the role of MRI in the evaluation of hip pain in pregnancy